commit be62c9be841c7959775062946e4d8c7e0a1b89f2 parent 3fbf829aa1e50e9da8ca05a480a53c7fd4add7f2 Author: miksa234 <milutin@popovic.xyz> Date: Thu, 28 Sep 2023 09:23:42 +0100 add dyn_sys Diffstat:
| A | dyn_sys/build/main.aux | | | 291 | ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | dyn_sys/build/main.fdb_latexmk | | | 230 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | dyn_sys/build/main.fls | | | 810 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | dyn_sys/build/main.log | | | 698 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | dyn_sys/build/main.toc | | | 57 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | dyn_sys/main.tex | | | 3457 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | dyn_sys/prog/.ipynb_checkpoints/prog_dynsys-checkpoint.ipynb | | | 56 | ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | dyn_sys/prog/prog_dynsys.ipynb | | | 363 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | dyn_sys/script.pdf | | | 0 | |
| A | dyn_sys/sheets/DSNDE_exam_4_6_2023.pdf | | | 0 | |
| A | dyn_sys/sheets/exercises_pt1.pdf | | | 0 | |
| A | dyn_sys/sheets/exercises_pt2.pdf | | | 0 | |
| A | dyn_sys/sheets/exercises_pt3.pdf | | | 0 | |
| A | dyn_sys/sheets/solutions.pdf | | | 0 |
14 files changed, 5962 insertions(+), 0 deletions(-)
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epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live +)) +Package pgfplots notification 'compat/show suggested version=true': document has been generated with the most recent feature set (\pgfplotsset{compat=1.18}). + +LaTeX Font Info: Trying to load font information for U+msa on input line 186. +(/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd +File: umsa.fd 2013/01/14 v3.01 AMS symbols A +) +LaTeX Font Info: Trying to load font information for U+msb on input line 186. + (/usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd +File: umsb.fd 2013/01/14 v3.01 AMS symbols B +) +LaTeX Font Info: Trying to load font information for U+wasy on input line 186. + (/usr/share/texmf-dist/tex/latex/wasysym/uwasy.fd +File: uwasy.fd 2020/01/19 v2.4 Wasy-2 symbol font definitions +) (build/main.toc [1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}]) +\tf@toc=\write4 +\openout4 = `main.toc'. + + +Overfull \hbox (6.24455pt too wide) in paragraph at lines 202--203 +[]$\OML/cmm/m/it/10 C[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 U; A\OT1/cmr/m/n/10 ) := \OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 f \OT1/cmr/m/n/10 : \OML/cmm/m/it/10 U \OMS/cmsy/m/n/10 ! \OML/cmm/m/it/10 A; f[]C[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 U; A\OT1/cmr/m/n/10 )\OMS/cmsy/m/n/10 g$\OT1/cmr/m/n/10 . + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 248--251 + + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 248--251 + + [] + +[2{/usr/share/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc}] [3] +Underfull \hbox (badness 10000) in paragraph at lines 356--357 + + [] + +[4] [5] [6] [7] +Underfull \hbox (badness 10000) in paragraph at lines 567--572 + + [] + +[8] [9] +Underfull \hbox (badness 10000) in paragraph at lines 685--688 + + [] + +[10] +Overfull \hbox (19.55449pt too wide) detected at line 751 +\OML/cmm/m/it/10 Q[] \OT1/cmr/m/n/10 = [][] = \OMS/cmsy/m/n/10 ^^@ [][] [][] \OML/cmm/m/it/10 dt \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 ^^@ [][] [][] \OML/cmm/m/it/10 C[] [][] dt \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 Q + [] + +[11] +Underfull \hbox (badness 10000) in paragraph at lines 765--766 + + [] + +[12] [13] [14] [15] [16] +Underfull \hbox (badness 10000) in paragraph at lines 1043--1044 + + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 1069--1071 + + [] + +[17] [18] [19] [20] [21] +Overfull \hbox (10.36708pt too wide) in paragraph at lines 1300--1303 +\OMS/cmsy/m/n/10 1$\OT1/cmr/m/n/10 . Then $(\OML/cmm/m/it/10 '\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 t[]; p\OT1/cmr/m/n/10 ))[] \OMS/cmsy/m/n/10 ^^R \OML/cmm/m/it/10 K$ \OT1/cmr/m/n/10 and there is a sub-se-quence $(\OML/cmm/m/it/10 '\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 t[]; p\OT1/cmr/m/n/10 ))[]$ such that $[][] \OML/cmm/m/it/10 '\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 t[]; p\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 2 + [] + +[22] [23] [24] [25] [26] [27] +Underfull \hbox (badness 10000) in paragraph at lines 1639--1643 + + [] + +[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] +Underfull \hbox (badness 10000) in paragraph at lines 2477--2481 + + [] + +[43] [44] +Underfull \hbox (badness 10000) in paragraph at lines 2596--2599 + + [] + +[45] [46] [47] [48] +Underfull \hbox (badness 10000) in paragraph at lines 2759--2764 + + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 2773--2777 + + [] + +[49] [50] [51] +Overfull \hbox (55.22473pt too wide) detected at line 2968 +[] \OT1/cmr/m/n/10 = [] = [] + [] + [] + [] + +[52] [53] [54] [55] [56] +Underfull \hbox (badness 10000) in paragraph at lines 3230--3234 + + [] + + +Overfull \hbox (26.64995pt too wide) in paragraph at lines 3252--3253 +[]\OT1/cmr/m/n/10 There ex-ists $\OML/cmm/m/it/10 x \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 Z[]$ \OT1/cmr/m/n/10 such that $\OML/cmm/m/it/10 T[]x \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 Z[]$ \OT1/cmr/m/n/10 for all $\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^U \OT1/cmr/m/n/10 2$. Take $\OML/cmm/m/it/10 ! \OT1/cmr/m/n/10 = 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; [] $\OT1/cmr/m/n/10 . + [] + +[57] +Underfull \hbox (badness 10000) in paragraph at lines 3276--3281 + + [] + +[58] [59] [60] [61] [62] (build/main.aux) ) +Here is how much of TeX's memory you used: + 27667 strings out of 477386 + 694944 string characters out of 5830686 + 1878388 words of memory out of 5000000 + 47410 multiletter control sequences out of 15000+600000 + 522844 words of font info for 73 fonts, out of 8000000 for 9000 + 475 hyphenation exceptions out of 8191 + 102i,11n,104p,813b,3158s stack positions out of 10000i,1000n,20000p,200000b,200000s 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+Output written on build/main.pdf (62 pages, 483087 bytes). +PDF statistics: + 315 PDF objects out of 1000 (max. 8388607) + 206 compressed objects within 3 object streams + 0 named destinations out of 1000 (max. 500000) + 13 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/dyn_sys/build/main.toc b/dyn_sys/build/main.toc @@ -0,0 +1,57 @@ +\babel@toc {english}{}\relax +\contentsline {section}{\numberline {0}Notations and conventions}{2}{}% +\contentsline {section}{\numberline {1}Part 1}{2}{}% +\contentsline {subsection}{\numberline {1.1}Modelling}{2}{}% +\contentsline {subsection}{\numberline {1.2}Autonomous ODE in $\mathbb {R}^n$}{3}{}% +\contentsline {subsection}{\numberline {1.3}Invariant subspaces}{8}{}% +\contentsline {subsection}{\numberline {1.4}Stability of equilibria}{14}{}% +\contentsline {subsection}{\numberline {1.5}Polar coordinates}{19}{}% +\contentsline {subsection}{\numberline {1.6}Asymptotic behavior}{21}{}% +\contentsline {paragraph}{Chlorine dioxide-Iodine-Malonic-Acid reaction: $(X = I, Y = ClO_2^-)$}{23}{}% +\contentsline {paragraph}{Hilbert's 16th problem:}{25}{}% +\contentsline {subsection}{\numberline {1.7}LaSalle's invariance principle}{25}{}% +\contentsline {subsection}{\numberline {1.8}Hamiltonian systems in 2D}{27}{}% +\contentsline {subsection}{\numberline {1.9}Special Hamiltonian systems: Newtonian systems}{28}{}% +\contentsline {subsection}{\numberline {1.10}Gradient systems in ${\mathbb {R}^n}$}{29}{}% +\contentsline {subsection}{\numberline {1.11}First integral (or constant of motion)}{30}{}% +\contentsline {subsection}{\numberline {1.12}How to find centers?}{33}{}% +\contentsline {subsubsection}{\numberline {1.12.1}Planar S-systems}{33}{}% +\contentsline {subsubsection}{\numberline {1.12.2}Reversible systems}{33}{}% +\contentsline {paragraph}{Reversibility with respect to $x = y$ line:}{34}{}% +\contentsline {subsection}{\numberline {1.13}Stable and unstable manifolds}{34}{}% +\contentsline {subsection}{\numberline {1.14}Center manifold}{36}{}% +\contentsline {paragraph}{Bad news:}{37}{}% +\contentsline {paragraph}{Good news:}{37}{}% +\contentsline {subsection}{\numberline {1.15}Andronov--Hopf bifurcation}{38}{}% +\contentsline {paragraph}{Back to 2d:}{42}{}% +\contentsline {section}{\numberline {2}Part 2}{42}{}% +\contentsline {subsection}{\numberline {2.1}Ideas from the General theory of dynamical systems}{42}{}% +\contentsline {subsubsection}{\numberline {2.1.1}Continuous vs. discrete time DS}{42}{}% +\contentsline {subsubsection}{\numberline {2.1.2}Continuous time systems can also give you discrete systems: $(\phi _t)_{t\geq 0}$ semiflows of $X$}{43}{}% +\contentsline {subsubsection}{\numberline {2.1.3}Relations between systems}{43}{}% +\contentsline {subsubsection}{\numberline {2.1.4}Example: Mathematical Billiards "table" $Q \subseteq \mathbb {R}^2$, open}{44}{}% +\contentsline {paragraph}{Poincare sections:}{44}{}% +\contentsline {subsubsection}{\numberline {2.1.5}Questions and structure}{44}{}% +\contentsline {paragraph}{Coarse structure:}{44}{}% +\contentsline {paragraph}{Topological dynamics:}{45}{}% +\contentsline {subsection}{\numberline {2.2}Circle rotations}{45}{}% +\contentsline {subsubsection}{\numberline {2.2.1}Rational rotation}{45}{}% +\contentsline {subsubsection}{\numberline {2.2.2}Irrational Rotations}{45}{}% +\contentsline {subsubsection}{\numberline {2.2.3}Linear flows on the $2$-torus $\mathbb {T}^2$}{45}{}% +\contentsline {subsubsection}{\numberline {2.2.4}Some notions of topological dynamics}{46}{}% +\contentsline {subsubsection}{\numberline {2.2.5}Distribution of orbits}{46}{}% +\contentsline {paragraph}{An application:}{48}{}% +\contentsline {subsubsection}{\numberline {2.2.6}More general circle maps}{49}{}% +\contentsline {subsubsection}{\numberline {2.2.7}Circle homeomorphisms with periodic points}{54}{}% +\contentsline {subsection}{\numberline {2.3}Maps with complicated orbit structure}{56}{}% +\contentsline {subsubsection}{\numberline {2.3.1}Warmup}{56}{}% +\contentsline {subsubsection}{\numberline {2.3.2}Basic properties}{56}{}% +\contentsline {paragraph}{Periodic orbits:}{56}{}% +\contentsline {paragraph}{Question:}{56}{}% +\contentsline {subsubsection}{\numberline {2.3.3}Symbolic dynamics and coding}{57}{}% +\contentsline {paragraph}{Application:}{57}{}% +\contentsline {paragraph}{Metric on $\Omega _2$:}{58}{}% +\contentsline {subsubsection}{\numberline {2.3.4}The general uniformly expanding circle maps $T:\mathbb {T}\to \mathbb {T}$ of degree 2}{58}{}% +\contentsline {subsection}{\numberline {2.4}Outlook: Coding for other systems}{59}{}% +\contentsline {paragraph}{Warning:}{60}{}% +\contentsline {subsubsection}{\numberline {2.4.1}Outlook: Measurable dynamics (Ergotic theory)}{60}{}% diff --git a/dyn_sys/main.tex b/dyn_sys/main.tex @@ -0,0 +1,3457 @@ +\documentclass{article} +\usepackage[utf8]{inputenc} +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage{amsthm} +%\usepackage[ngerman]{babel} +\usepackage[english]{babel} +\usepackage{geometry} +\usepackage{cases} +\usepackage{wasysym} +\usepackage{enumitem} +\usepackage{thmtools} +\usepackage{tikz} +\usepackage{pgfplots} +\usepgfplotslibrary{polar} +\pgfplotsset{compat = newest} + +\usetikzlibrary{angles,quotes} % for pic (angle labels) +\usetikzlibrary{arrows.meta} +\usetikzlibrary{calc} +\usetikzlibrary{decorations.markings} +\usetikzlibrary{bending} + +\tikzstyle{xline}=[black,thick,smooth] +\tikzstyle{width}=[{Latex[length=5,width=3]}-{Latex[length=5,width=3]},thick] +\tikzstyle{mydashed}=[dash pattern=on 1.7pt off 1.7pt] + +\tikzset{>=latex} +\tikzset{ + traj/.style 2 args={xline,postaction={decorate},decoration={markings, + mark=at position #1 with {\arrow{<}}, + mark=at position #2 with {\arrow{<}}} + } +} + +\geometry{ + left=3cm, + right=3cm, + top=2cm, + bottom=4cm, + bindingoffset=5mm +} + + +\newcommand*{\N}{\mathbb{N}} +\newcommand*{\Z}{\mathbb{Z}} 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\\#13 +%\end{pmatrix}} + +\newcommand*{\matutwo}[3]{\begin{pmatrix} + #1\\ \\ +\end{pmatrix}} +\newcommand*{\matuthree}[6]{\begin{pmatrix} + #1\\ \\ & +\end{pmatrix}} + +\newcommand*{\matdiagtwo}[2]{\mattwo{#1}{\,}{\,}{#2}} +\newcommand*{\matdiagthree}[3]{\matthree{#1}{\,}{\,}{\,}{#2}{\,}{\,}{\,}{#3}} + +\newcommand{\matdoublediagthree}[5]{\matthree{#1}{#2}{\,}{\,}{#3}{#4}{\,}{\,}{#5}} + +\newcommand{\quests} +{ +Modelling +Autonomous ODE in R^n +Invariant subspaces +Stability of equilibria +Polar coordinates +Asymptotic behavior +LaSalle's invariance principle +Hamiltonian systems in 2D +Special Hamiltonian systems: Newtonian systems +Gradient systems in R^n +First integral (or constant of motion) +How to find centers +Stable and unstable manifolds +Center manifold +Andronov bifurcation + +Ideas from the General theory of dynamical systems +* (Def 2.29) Circle rotations +Maps with complicated orbit structure +Outlook: Coding for other systems +} + +\declaretheorem[ + name=Theorem, + numberwithin=section + ]{thm} +\declaretheorem[ + name=Lemma, + sibling=thm, + ]{lem} +\declaretheorem[ + name=Proposition, + sibling=thm, + ]{prop} +\declaretheorem[ + name=Corollary, + sibling=thm, + ]{cor} + +\declaretheorem[ + name=Definition, + style=definition, + sibling=thm, + numbered=yes, + ]{defin} + +\declaretheorem[ + name=Remark, + style=remark, + numbered=no + ]{rem} +\declaretheorem[ + name=Recall, + style=remark, + numbered=no + ]{rec} +\declaretheorem[ + name=Example, + style=remark, + numbered=no + ]{exam} +\declaretheorem[ + name=Notation, + style=remark, + numbered=no + ]{notation} +\declaretheorem[ + name=Homework, + style=remark, + numbered=no + ]{hw} + + +\title{Dynamical Systems and Nonlinear Differential Equations 2023S \\ +Lecturers: Roland Zweimüller, Balázs Boros} +\author{Nikolas Hauschka} +\date{} + +\begin{document} + +\maketitle +\tableofcontents + +\setcounter{section}{-1} + +\section{Notations and conventions} + +For simplicity, we use some notations and conventions, which aren't always specified. If not otherwise specified, we use the following things: + +\begin{enumerate} + \item $U$ and $V$ are open sets. + + \item $U$ and $V$ are subsets of $\Rn$. + + \item For $A \subseteq \Rn$ we define $C^0(U,A) := C(U,A) := \{f:U \to A, f \text{ is continuous}\}$. + + \item $C^{d+1}(U,A) := \{f:U\to A, f \text{ is differetiable and each first partial derivative lies in } C^d(U,A)\}$. + + \item If $A = \Rn$ then we might write $C^d(U)$ instead of $C^d(U,\Rn)$. + + \item For $m,n\in\Z$ with $m\leq n$, we define $\jbr{m,n}:=\{m,\dots,n\}=[m,n]\cap\Z$. + + \item We also might write $\jbr{n}$ instead of $\jbr{1,n}$. + + \item We use $\N := \{0,1,\dots\}$ and $\Ns:=\{1,2,\dots\}$. + + \item We define $\T := \R / \Z$, which can be viewed as the interval $[0,1]$ where the ends are identified. + + \item If an element of $\T$ is added/subtracted/multplied with an element of $\R$, the result is the corresponding element of $\T \pmod1$. We won't always state that it's calculated $\pmod1$. + + \item For $a,b \in \T$ with $b<a$ the interval we define the interval $[a,b] := [a,1) \cup [0,b]$ if not otherwise stated. +\end{enumerate} + +\section{Part 1} + +\subsection{Modelling} + +When modeling we have to make certain decisions. Some types of models are listed below. + +\begin{itemize} + \item Continuous time or discrete time. + + \item Deterministic or stochastic. + + \item State space: + \begin{itemize} + \item finite, discrete + + \item metric space + + \item Euclidean space (finite dimensional) + + \item Hilbert space + \end{itemize} + + \item Homogeneous (ODE) or inhomogeneous (PDE) + + \item Future depends only on the present or also on the past. + + \item autonomous or non-autonomous +\end{itemize} + +In this lecture we choose: Continuous time, deterministic, Euclidean space, only on the present, autonomous. +\newline +\newline +\subsection{Autonomous ODE in $\R^n$} +\begin{thm} + Given + $$\dot x(t) = f(x(t))$$ + where $f:U \to \R^n$ is locally Lipschitz continuous. Then for all $p \in U$ there exists a unique solution $t\mapsto \phi(t,p)$ on a maximal interval such that $\phi(0,p) = p$. +\end{thm} + +Details can be found in the book "Differential Equations and dynamical systems" by Perko. + +\begin{exam}[Lotka reactions] + $$\begin{array}{rcl} + X &\stackrel{\kappa_1}{\to}& 2X\\ + X+Y &\stackrel{\kappa_2}{\to}& 2Y\\ + Y &\stackrel{\kappa_3}{\to}& 0 + \end{array}$$ + + $$\begin{array}{rcccl}\dot x &=&\kappa_1x-\kappa_2xy &=& x(\kappa_1-\kappa_2y)\\ + \dot y&=&\kappa_2xy-\kappa_3y &=& y(\kappa_2x-\kappa_3)\\ + &&\kappa_1,\kappa_2, \kappa_3 &>& 0 + \end{array}$$ + Let's go through the details. The line $X \stackrel{\kappa_1}{\to} 2X$ that the species of type $X$ doubles at the rate $\kappa_1$. So it makes sense to get an equation like $\dot x =\kappa_1x$. The third line is similar except that the species of type $Y$ decreases with a rate of $\kappa_3$. So we get an equation like $\dot y=-\kappa_3y$. The second line is more complicated. Here the transformation occurs at a rate of $\kappa_2$ when two species of the different types meet. If the $X$ count or the $Y$ is doubled then there are twice as many meetings between $X$ and $Y$ so the expression $\kappa_2xy$ makes sense. By this transformation the $Y$ count increases while the $X$ count decreases, so we have to add $\kappa_2xy$ to the $\dot y$-equation and subtract it from the $\dot x$-equation. +\end{exam} + +\begin{exam}[Ivanova reactions] + $$\begin{array}{rcl}Z+X &\stackrel{\kappa_1}{\to}& 2X\\ + X+Y &\stackrel{\kappa_2}{\to}& 2Y\\ + Y+Z &\stackrel{\kappa_3}{\to}& 2Y + \end{array}$$ + + + + $$\begin{array}{rcl}\dot x &=& x(\kappa_1z - \kappa_2y)\\ + \dot y &=& y(\kappa_2x - \kappa_3z)\\ + \dot z &=& z(\kappa_3y - \kappa_1x)\end{array}$$ +\end{exam} + +\begin{exam}[Competitive Lotka-Volterra systems (two competing species)] + $$\dot x=x(r_1+b_{11}x+b_{12}y)$$ + $$\dot y=y(r_2+b_{21}x+b_{22}y)$$ + With the parameters $r_j > 0, b_{ij} < 0$ for $i,j = 1,2$. +\end{exam} + +\begin{exam}[Cyclic competition of three species.] + $$\begin{array}{rcl}\dot x &=& x(1-x-\alpha y-\beta z)\\ + \dot y &=& y(1-\beta x-y-\alpha z)\\ + \dot z &=& x(1-\alpha x-\beta y-z) + \end{array}$$ + With the parameters $\alpha,\beta > 0$ and the restriction $x,y,z \geq 0$. +\end{exam} + +\begin{exam}[Lotka-Volterra equation] + $$\dot x_i = x_i\left(r_i+\sum_{l = 1}^n b_{i,l}x_l\right), i\in\jbr{n}$$ + With the parameters $r \in \R^n, B \in \R^{n\times n}$ and the restriction $x \in \R^n_{\geq 0}$. +\end{exam} + +\begin{exam}[Replicator dynamics on the simplex (e.g. rock-paper-scissors)] + $$\dot x_i = x_i((Ax)_i-x^TAx), i \in\jbr{n}$$ + With $A \in \R^{n\times n}$ and the restriction $x\in\R_{\geq0}^n$ such that $\sum_{j=1}^n x_j = 1$. +\end{exam} + +\begin{exam}[Pendulum] + Newton's second law of motion. + $$\begin{aligned}F &= ma\\ + -mg\sin(x)&=ml\ddot x\\ + \ddot x + \frac{g}{l}\sin(x)&=0\end{aligned}$$ +\end{exam} + +\begin{exam}[Van der Pol oscilator (electrical engineering)] + $$\ddot x-\mu(1-x^2)\dot x+x=0$$ + With the parameter $\mu \in \R$ and the restriction $x\in\R_{\geq0}$. +\end{exam} + +\begin{exam}[SIR (epidemiology): $S \to I \to R$] + The population can be divided into three groups:\\ + $S:$ susceptible\\ + $I:$ infected\\ + $R:$ recovered + $$\begin{array}{rcl}\dot S&=&-\beta SI\\ + \dot I&=&\beta SI - \gamma I\\ + \dot R&=&\gamma I + \end{array}$$ + Where $\beta > 0$ is the rate of transmission, $\gamma > 0$ is the rate of recovery and $S+I+R$ is constant. +\end{exam} + +\begin{exam}[Two body problem] + Here $r_1(t),r_2(t) \in \R^3$ describe the positions, $\dot r_1(t), \dot r_2(t) \in \R^3$ describe the velocities and $\ddot r_1(t),\ddot r_2(t) \in \R^3$ describe the accelerations. Also $m_1$ and $m_2$ are the masses and $\gamma > 0$ is the gravitational constant. + $$m_1\ddot r_1 = - \frac{\gamma m_1 m_2}{|r_2-r_1|^3}(r_1-r_2)$$ + $$m_2\ddot r_2 = - \frac{\gamma m_1 m_2}{|r_2-r_1|^3}(r_2-r_1)$$ +\end{exam} + +\begin{exam}[Lorenz equation] + $$\begin{array}{rcl}\dot x &=& \sigma(y-x)\\ + \dot y &=& \rho x-y-xz\\ + \dot z &=& xy-\beta z + \end{array}$$ + Where $\sigma,\rho, \beta > 0$ and $x,y,z \in \R$. It shows chaos for $\sigma = 10, \rho = 28, \beta=\frac83$. +\end{exam} + +\begin{exam}[Linear ODEs] + $$\dot x(t) = Ax(t)$$ + Where $x(t)\in \R^n$ and $A \in \R^{n \times n}$. The solution is the function $x: \R \to \R^{n}$ with $x(t)=e^{At}x(0)$ for all $t$, where + $$e^{At}:=\sum_{k=0}^\infty\frac{t^k}{k!}A^k.$$ +\end{exam} + +\begin{thm}[Real Jordan normalform] + For any $A \in \R^{n\times n} $ there is an invertible $P \in \R^{n \times n}$, such that $B = P^{-1}AP$ is a block diagonal matrix with blocks of the form\\ + $$\matdoublediagthree\lambda1\ddots1\lambda \text{ or } \matdoublediagthree{D}{I_2}{\ddots}{I_2}{D},$$ + where $\lambda \in \sigma(A)\cap \R$ or $\mu \pm i\omega \in \sigma(A)\setminus\R$ ($\sigma(A)$ is the set of the generalized eigenvalues of $A$) and + $$D = \mattwo\mu{-\omega}\omega\mu, \quad I_2=\mattwo1001.$$ +\end{thm} + +\begin{cor} + Suppose that $P,B$ are as above. Then + $$x(t)=Pe^{Bt}P^{-1}x(0).$$ +\end{cor} + +\begin{prop} + If + $$B = \matdoublediagthree{\lambda}{1}{\ddots}{1}{\lambda} \in \mathbb{R}^{m \times m}$$ + then + $$e^{Bt} = e^{\lambda t}\matuthree1\dots{\frac{t^{m-1}}{(m-1)!}}\ddots\vdots1.$$ + If + $$B = \matdoublediagthree{D}{I_2}{\ddots}{I_2}{D} \in \mathbb{R}^{2m \times 2m}$$ + then + $$e^{Bt}=e^{\mu t}\matuthree R\dots{\frac{Rt^{m-1}}{(m-1)!}}\ddots\vdots R,$$ + where + $$R = \mattwo{\cos(\omega t)}{-\sin(\omega t)}{\sin(\omega t)}{\cos(\omega t)}.$$ +\end{prop} + +\begin{cor} + Each coordinate of each solution of $\dot x = Ax$ is a linear combination of $e^{\mu t}t^k\cos(\omega t)$ or $e^{\mu t}t^k\sin(\omega t)$, where $\mu\pm i \omega \in \sigma(A)$ and $k$ is smaller than the multiplicity of $\lambda$ in the minimal polynomial of $A$. +\end{cor} + +Let $n = 2$. Then we have the following cases: +\begin{itemize} + \item If $B = \matdiagtwo\lambda\mu$ then $e^{Bt} = \matdiagtwo{e^{\lambda t}}{e^{\mu t}}$. + + \item If $B = \matutwo\lambda1\lambda$ then $e^{Bt}=e^{\lambda t}\matutwo1t1$. + + \item If $B = \mattwo\mu{-\omega}\omega\mu$ then $e^{Bt}=e^{\mu t}\mattwo{\cos(\omega t)}{-\sin(\omega t)}{\sin(\omega t)}{\cos(\omega t)}$. +\end{itemize} + +Depending on the case, the diagram looks different. + +\begin{enumerate} + \item Saddle: $\matdiagtwo\lambda\mu$ with $\lambda < 0 < \mu$. + The flow moves towards the origin on the horizontal axis and moves away on the vertical axis. + + \begin{tikzpicture} + \begin{axis}[ + xmin = -4, xmax = 4, + ymin = -4, ymax = 4, + zmin = 0, zmax = 1, + axis equal image, + view = {0}{90}, + samples = 9, + samples y = 9, + ] + + \addplot3[ + quiver = { + u = {-x}, + v = {y}, + scale arrows = 0.25, + }, + -stealth, + ] {0}; + \end{axis} + \end{tikzpicture} + + \item Stable nodes: + + \begin{itemize} + \item $B=\begin{pmatrix} + \lambda & 0\\ + 0 & \mu + \end{pmatrix}$ with $\lambda = \mu < 0$. + + \begin{tikzpicture} + \begin{axis}[ + xmin = -4, xmax = 4, + ymin = -4, ymax = 4, + zmin = 0, zmax = 1, + axis equal image, + view = {0}{90}, + samples = 9, + samples y = 9, + ] + + \addplot3[ + quiver = { + u = {-x}, + v = {-y}, + scale arrows = 0.25, + }, + -stealth, + ] {0}; + \end{axis} + \end{tikzpicture} + + \item $B=\begin{pmatrix} + \lambda & 0\\ + 0 & \mu + \end{pmatrix}$ with $\lambda < \mu < 0$. + + \begin{tikzpicture} + \begin{axis}[ + xmin = -4, xmax = 4, + ymin = -4, ymax = 4, + zmin = 0, zmax = 1, + axis equal image, + view = {0}{90}, + samples = 9, + samples y = 9, + ] + + \addplot3[ + quiver = { + u = {-2*x}, + v = {-y}, + scale arrows = 0.25, + }, + -stealth, + ] {0}; + \end{axis} + \end{tikzpicture} + + \item $B=\begin{pmatrix} + \lambda & 1\\ + 0 & \lambda + \end{pmatrix}$ with $\lambda < 0$. + + \begin{tikzpicture} + \begin{axis}[ + xmin = -4, xmax = 4, + ymin = -4, ymax = 4, + zmin = 0, zmax = 1, + axis equal image, + view = {0}{90}, + samples = 9, + samples y = 9, + ] + + \addplot3[ + quiver = { + u = {-x+y}, + v = {-y}, + scale arrows = 0.25, + }, + -stealth, + ] {0}; + \end{axis} + \end{tikzpicture} + \end{itemize} + + The flow moves towards the origin from all sides. + + \item Focus: $\begin{pmatrix} + \mu & -\omega\\ + \omega & \mu + \end{pmatrix}$ with $\omega \neq 0, \mu \neq 0$. + + \begin{tikzpicture} + \begin{axis}[ + xmin = -4, xmax = 4, + ymin = -4, ymax = 4, + zmin = 0, zmax = 1, + axis equal image, + view = {0}{90}, + samples = 9, + samples y = 9, + ] + + \addplot3[ + quiver = { + u = {x-y}, + v = {x+y}, + scale arrows = 0.25, + }, + -stealth, + ] {0}; + \end{axis} + \end{tikzpicture} + + The flow moves around the origin and moves closer or further away from it (depending on the sign of $\mu$). + + \item Center: $\begin{pmatrix} + \mu & -\omega\\ + \omega & \mu + \end{pmatrix}$ with $\omega \neq 0, \mu = 0$. + + \begin{tikzpicture} + \begin{axis}[ + xmin = -4, xmax = 4, + ymin = -4, ymax = 4, + zmin = 0, zmax = 1, + axis equal image, + view = {0}{90}, + samples = 9, + samples y = 9, + ] + + \addplot3[ + quiver = { + u = {-y}, + v = {x}, + scale arrows = 0.25, + }, + -stealth, + ] {0}; + \end{axis} + \end{tikzpicture} + + The flow moves periodically around the origin in circles. +\end{enumerate} + +If $0 \in \sigma(A)$ then the origin is not an isolated equilibrium.\\ +%Bifurcation diagram.\\ +\newline +Let $\delta = \det(A)$ and $\tau = \tr(A)$. Then the characteristic polynomial of $A$ is: $x^2-\tau x + \delta$. +Given +$$\dot x = Ax$$ +we define $B := P^{-1}AP$ and $y := P^{-1}x$. Then we get +$$\dot y = P^{-1}\dot x = P^{-1}Ax = P^{-1}APy = By.$$ + +\subsection{Invariant subspaces} + +\begin{defin} + Let $A\in\C^{n\times n}$ and $\lambda \in \sigma(A), v \in \C^n$ is a generalized eigenvector, if + $$(\lambda I-A)^kv=0$$ + for some $k\in\Ns$. +\end{defin} + +\begin{thm} + Let $A\in \R^{n\times n}$ with eigenvalues as follows: + \begin{itemize} + \item $\lambda_1,\dots,\lambda_k\in\R$ + + \item $\lambda_j=\mu_j+i\omega_j, \overline{\lambda_j}=\mu_j-i\omega_j, \quad j\in\jbr{k+1,m}\quad (2m-k=n)$ + \end{itemize} + + Then the set $\{u_1,\dots,u_k,u_{k+1},v_{k+1},\dots,u_m,v_m\}$ is a basis of $\R^n$, where $u_1, \dots,u_k$ are generalized eigenvectors corresponding to $\lambda_1, \dots, \lambda_k$ and the $u_j\pm i v_j$ are generalized eigenvectors corresponding to the $\mu_j \pm i\omega_j$ where $j\in\jbr{k+1,m}$. +\end{thm} + +\begin{defin} + We define the following subspaces: + \begin{itemize} + \item Stable subspace: $E^s=\spanl\{u_j,\nu_j:\Re(\lambda_j)<0\}$. + + \item Center subspace: $E^c=\spanl\{u_j,\nu_j:\Re(\lambda_j)=0\}$. + + \item Unstable subspace: $E^u=\spanl\{u_j,\nu_j:\Re(\lambda_j)>0\}$. + \end{itemize} + We also define: + \begin{itemize} + \item $s(A) = \dim(E^s)$ + + \item $c(A) = \dim(E^c)$ + + \item $u(A) = \dim(E^u)$ + \end{itemize} +\end{defin} + +\begin{exam} + Given + $$\begin{aligned} + \dot x&=-2x-y\\ + \dot y &= x-2y\\ + \dot z &= 3z, + \end{aligned}$$ + we can read the matrix + $$A=\matthree{-2}{-1}{0}{1}{-2}{0}{0}{0}{3}.$$ + We get the following eigenpairs: + \begin{itemize} + \item $\lambda_1 = 3, \quad u_1 =\vecthree001$ + + \item $\lambda_2 = -2+i, \quad u_2+iv_2 = \vecthree010+i\vecthree100$ + \end{itemize} + Also + $$\begin{array}{ll}E^s=(x,y)-\text{plane}, &\quad s(A) = 2,\\ + E^c=\{0\}, &\quad c(A)=0,\\ + E^u=z-\text{axis}, &\quad u(A)=1. + \end{array}$$ +\end{exam} + +\begin{exam} + Given + $$\begin{array}{rcl} + \dot x &=& -y\\ + \dot y &=& x\\ + \dot z &=& 2z, + \end{array}$$ + we can read the matrix + $$A=\matthree{0}{-1}{0}{1}{0}{0}{0}{0}{2}$$ + We get the following eigenpairs: + \begin{itemize} + \item $\lambda_1=2, \quad u_1=\vecthree001$ + + \item $\lambda_2=i, \quad u_2+iv_2=\vecthree010+i\vecthree100$ + \end{itemize} + $\begin{array}{ll}E^s=\{0\},\\E^c=(x,y)-\text{plane},\\ + E^u=z-\text{axis}. + \end{array}$ +\end{exam} + +\begin{exam} + Given + $$\dot x=0$$ + $$\dot y = x,$$ + we can read the matrix + $$A=\mattwo0010$$ + Since $(A-0)^2 = 0$, we get the following eigenpairs: + \begin{itemize} + \item $\lambda_1=0, \quad u_1=\vectwo01$ + + \item $\lambda_2=0, \quad u_2\vectwo10$. + \end{itemize} + $\begin{array}{ll}E^s=\{0\},\\ + E^c=(x,y)-\text{plane},\\ + E^u=\{0\}. + \end{array}$ +\end{exam} + +\begin{thm} + The whole space is a direct sum of the three subspaces, meaning $\R^n=E^s\oplus E^c \oplus E^u$. Also the following statements hold: + \begin{itemize} + \item $E^i$ is invariant ($i = s,c,u)$.\\ + If $x(0)\in E^i$ then $x(t)=e^{At}x(0)\in E^i$ for all $t \in \R$. + + \item If $x(0) \in E^s$ then $x(t) \to 0$ as $t\to \infty$. Moreover there exist $K,\alpha > 0$, such that + $$\|e^{At}\| \leq Ke^{-\alpha t}$$ + for all $ t \geq 0$. + + \item If $x(0)\in E^u$ then $x(t) \to 0$ as $t \to -\infty$. Moreover there exist $L,\beta > 0$, such that + $$\|e^{At}\|\leq Le^{\beta t}$$ + for all $t\leq 0$.\\ + %$|x(t)|\leq Le^{\beta t}|x(0)| \forall t \leq 0$ + \item $E^s = \{ p \in \R^n:e^{At}p \to 0$ as $t \to \infty\}$ + \item $E^u = \{ p \in \R^n:e^{At}p \to 0$ as $t \to -\infty\}$ + \end{itemize} +\end{thm} + +\begin{defin} + We say that a matrix $A$ is stable if $\Re(\lambda) < 0$ for all $\lambda \in\sigma(A)$. +\end{defin} + +\begin{itemize} + \item For $n=2$ the matrix $A$ is stable if and only if $\det(A) > 0$ and $\tr(A) < 0$. The characteristic polynomial is $\lambda^2-\tr(A)\lambda+\det(A)$. + + %\det(A)>M\tr(A) + \item For $n=3$ the matrix $A$ is stable if and only if $\det(A) < 0, \tr(A)< 0,M>0$, where $M$ is the sum of the $2\times2$ principal minors + $$M =\det\mattwo{a_{11}}{a_{12}}{a_{21}}{a_{22}} + \det\mattwo{a_{11}}{a_{13}}{a_{31}}{a_{33}}+\det\mattwo{a_{22}}{a_{23}}{a_{32}}{a_{33}}.$$ + The characteristic polynomial is (up to the faktor $(-1)$) $\lambda^3 -\tr(A)\lambda^2+M\lambda-\det(A)$. +\end{itemize} + + +\begin{thm}[Routh-Hurwitz] + Each root of $x^n+b_{n-1}x^{n-1}+\dots +b_1x+b_0$ has a negative real part if and only if all the leading principal minors of $H$ are positive, where + $$H := \begin{pmatrix} + b_{n-1} & 1 & 0 & 0 & 0 & 0 & 0 & \dots & 0\\ + b_{n-3} & b_{n-2} & b_{n-1} & 1 & 0 & 0 & 0 & \dots & 0\\ + b_{n-5} & b_{n-4} & b_{n-3} & b_{n-2} & b_{n-1} & 1 & 0 & \dots & 0\\ + \vdots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \vdots\\ + 0 & \dots & 0 & 0 & b_0 & b_1 & b_2 & b_3 & b_4\\ + 0 & \dots & 0 & 0 & 0 & 0 & b_0 & b_1 & b_2\\ + 0 & \dots & 0 & 0 & 0 & 0 & 0 & 0 & b_0 + \end{pmatrix}.$$ +\end{thm} +Applying this to $\det(xI-A)$, we get +\begin{itemize} + \item $b_0 = (-1)^n\det(A)$ + + \item $b_{n-1} = -\tr(A)$ + + \item $b_j=(-1)^{n-j}\sum_{\alpha\subseteq \jbr{n}, |\alpha|=n-j} A[\alpha|\alpha]$\\ + The sum of principal minors corresponding to the rows/columns in $\alpha$. +\end{itemize} + +\begin{thm}[Lyapunov] + For $A\in \R^{n\times n}$. The following are equivalent: + \begin{enumerate} + \item $A$ is stable. + + \item There is a symmetric $Q>0$, such that $QA+A^TQ < 0$. + + \item For every symmetric $C <0$ there is a symmetric $Q>0$ such that $QA+A^TQ=C$. + \end{enumerate} +\end{thm} + +\begin{proof} + We prove $(2) \Rightarrow (1) \Rightarrow (3) \Rightarrow (2)$. + \begin{itemize} + \item $(2) \Rightarrow (1)$: Let $Q$ be as in the statement. Now we take the time derivative of $x^TQx$. For better readability, we write $x$ instead of $x(t)$. + $$\frac{d}{dt}(x^TQx) = \dot x^TQx+x^TQ\dot x = x^TA^TQx+x^TQAx = x^T(QA+A^TQ)x.$$ + The last expression is negative if $x(t) \neq 0$. The level sets $\{x \in \R^n: x^TQx = \gamma\}$ for $\gamma > 0$ are ellipsoids and solutions are going inwards, because if the time increases then $x^TQx$ decreases. Therefore $x(t) = e^{At}p\to 0$ as $t\to\infty$ for all $p \in \R^n$. So we get $E^s = \R^n$ and $A$ is stable. + + \item $(1)\Rightarrow (3):$ Let $C < 0$ be a symmetric matrix. Let + $$Q = -\int_0^\infty e^{A^Tt}Ce^{At}dt.$$ It exists and is finite, because $\|e^{At}\|\leq Ke^{-\alpha t}$ for $t\geq 0$. + \begin{itemize} + \item Clearly $Q=Q^T>0$, because + $$Q^T = \left(-\int_0^\infty e^{A^Tt}Ce^{At}dt\right)^T = -\int_0^\infty\left(e^{A^Tt}Ce^{At}\right)^Tdt= -\int_0^\infty\left(e^{At}\right)^TC^T\left(e^{A^Tt}\right)^Tdt = Q$$ + and + $$x^TQx = -\int_0^\infty x^Te^{A^Tt}Ce^{At}xdt = -\int_0^\infty \left(e^{A^Tt}x\right)^TCe^{At}xdt = -\int_0^\infty y^TCydt > 0.$$ + + \item We also note that + $$QA+A^TQ = -\int_0^\infty e^{A^Tt}Ce^{At}A+A^Te^{A^Tt}Ce^{At}dt = -\int_0^\infty \frac{d}{dt}(e^{A^Tt}Ce^{At})dt =$$ + $$=-[e^{A^Tt}Ce^{At}]_{t=0}^{t=\infty} = -(0-C)=C.$$ + \end{itemize} + + \item $(3)\Rightarrow (2)$: Trivial. + \end{itemize} +\end{proof} + +\begin{defin} + For $k \in\Ns$, we say that $h:U\to V$ is a homeomorphism (or $C^k$-diffeomorphism) if it is bijective and $h,h^{-1}$ are continuous (or $C^k$).\\ +\end{defin} + +\begin{defin}[Flow] + Let $f \in C^1(U)$. Denote the solution of + $$\begin{aligned}\dot x(t) &= f(x(t))\\ + x(0) &= p\end{aligned}$$ + by $t \mapsto \varphi(t,p)$.\\ + The flow of $\dot x=f(x)$ is + $$\varphi_t:\{p\in U: t\in I(p)\} \to U$$ + $$p \mapsto \varphi(t,p)$$ + For fixed $t$, the set $\varphi_t(K)$ is where a set $K$ is moved after time $t$ (as opposed to $\{\varphi(t,p)\colon t \in I(p)\}$, which is the trajectory of a single point $p$). +\end{defin} + +For $\dot x = Ax$, the flow is $\varphi_t = e^{At}:\R^n\to\R^n$. + +\begin{prop} + The flow has the following properties (where these make sense): + \begin{enumerate} + \item $\varphi_0=id$ + + \item $\varphi_s\circ\varphi_t = \varphi_{t+s}$ + + \item $\varphi_t\circ\varphi_{-t}=id$ + \end{enumerate} +\end{prop} + +\begin{defin}[Conjugate flow] + We have the following ODEs + $$\dot x=f(x)$$ + in $U$ with the flow $\varphi_t$ and + $$\dot y=g(y)$$ + in $V$ with the flow $\psi_t$.\\ + We say that the flows $\varphi_t$ and $\psi_t$ are topologically conjugate if there is a homeomorphism $h:U\to V$ such that $h\circ \varphi_t=\psi_t\circ h$. If $h$ is a $C^k$-diffeomorphism, we say $\varphi_t$ and $\psi_t$ are $C^k$ conjugate. +\end{defin} + +\begin{thm} + If the matrices $A,B \in\R^{n\times n}$ are stable then the flows $e^{At}, e^{Bt}$ are topologically conjugate. (There is a homeomorphism $\R^n\to\R^n$ such that $h(e^{At}p)=e^{Bt}h(p)$ for all $p\in\R^n$ and $t\in\R$.) +\end{thm} + +\begin{proof}[Sketch of the proof.] + Without loss of generality, assume $B = -I$ (because being topological conjugate is an equivalence relation). Because $A$ is stable, we can find a symmetric $Q > 0$ satisfying $QA+A^TQ < 0$. Let + $$S = \{p\in\R^n:p^TQp=1\}.$$ + Then for all $p \in \R^n\setminus \{0\}$ there is a unique $\tau(p)$ such that $e^{A\tau(p)}p\in S$. It exists, because $e^{At}p$ approaches $0$ at $\infty$ and $\infty$ at $-\infty$ and the flow is continuous. It is unique because the time derivative of $x(t)^TQx(t)$ is negative (see proof of the Lyapunov theorem). Then $\tau:\R^n \setminus\{0\} \to \R$ is continuous (because solutions depend on the initial conditions continuously).\\ + %$$e^{A\tau(e^{At}p)}\left(e^{At}p\right) = e^{A(\tau(e^{At}p)+t)}p = e^{A\tau(p)}p,$$ + Since $p$ and $e^{At}p$ are on the same orbit with a time difference of $t$, we know that + $$\tau(e^{At}p)=\tau(p)-t.$$ + Define + $$h(p) := \begin{cases} + e^{(A+I)\tau(p)}p&p \neq 0\\ + 0&p=0. + \end{cases}$$ + The orbits are mapped to orbits: Indeed, for $p\neq 0$ we get + $$h(e^{At}p)=e^{(A+I)\tau(e^{At}p)}e^{At}p = e^{(A+I)(\tau(p)-t)}e^{At}p = e^{-It}e^{(A+I)\tau(p)}p = e^{-It}h(p).$$ + We omit the proof that $h$ is a homeomorphism. +\end{proof} + +Hence, a stable focus and a stable node are topologically conjugate. + +\begin{defin} + We say that $A\in \R^{n\times n}$ is hyperbolic if $\Re(\lambda) \neq 0$ for all $\lambda \in \sigma(A)$. +\end{defin} + +\begin{thm} + For $A, B \in \R^{n\times n}$ hyperbolic matrices, the following statements are equivalent: + \begin{itemize} + \item $s(A) = s(B)$ and $u(A) = u(B)$ + + \item $e^{At}$ and $e^{Bt}$ are topologically conjugate. + \end{itemize} +\end{thm} + +\begin{exam} + The matrices + $$A = \mattwo{0}{-2}{2}{0}, \quad B=\mattwo{0}{-1}{1}{0}$$ + are not topologically conjugate. To show this, we compute + $$e^{At} = \mattwo{\cos(2t)}{-\sin(2t)}{\sin(2t)}{\cos(2t)}, \quad e^{Bt} = \mattwo{\cos(t)}{-\sin(t)}{\sin(t)}{\cos(t)}.$$ + Suppose that there is a homeomorphism $h$ such that + $$h(e^{At}p) = e^{Bt}h(p)$$ + for all $p\in\R^2$ and for all $t\in \R$. Setting $t = \pi$ yields $h(p)= -h(p)$ and then $h(p) = 0$ for all $p \in \R^2$, which is a contradiction. +\end{exam} + +\begin{thm} + If $c(A) = c(B) =n$ then $e^{At}$ and $e^{Bt}$ are topologically conjugate if and only if $A$ and $B$ are similar matrices. +\end{thm} + +\begin{thm} + The flows $e^{At}, e^{Bt}$ are topologically conjugate if and only if $s(A) = s(B), u(A) = u(B), c(A) = c(B)$ and $A|_{E^c(A)}, B|_{E^c(B)}$ are similar. +\end{thm} + +\begin{prop} + $A$ and $B$ are $C^1$-conjugate if and only if $A$ and $B$ are similar. +\end{prop} + +\begin{proof} + We need to show both directions. + \begin{itemize} + \item $\Leftarrow$: We just use the transformation matrix as a homeomorphism. + + \item $\Rightarrow$: By definition $h(e^{At}p)=e^{Bt}h(p)$ for all $t,p$. Differentiate with respect to $p$ and set $p = 0$. + $$h'(e^{At}0)e^{At}=e^{Bt}h'(0)$$ + $$h'(0)e^{At}=e^{Bt}h'(0),$$ + where $h'$ is the Jacobian matrix of $h$. Differentiate with respect to $t$ and set $t=0$. + $$h'(0)Ae^{A0}=Be^{B0}h'(0)$$ + Let $P := (h'(0))^{-1}$. Then + $$B=P^{-1}AP.$$ + \end{itemize} +\end{proof} + +Hence $C^1$-conjugacy is too strong: e.g. + +$$\dot x = -x$$ +and +$$\dot y = -2y$$ +are not $C^1$-conjugate. + +\begin{rem}[Related to Routh-Hurwitz] + Given the real polynomial $x^n+b_{n-1}x^{n-1} +\dots + b_0$, where all roots have negative real parts. Then $b_{n-1} > 0, \dots, b_0 > 0$. +\end{rem} + +\begin{proof} + We first consider the simplest cases. + \begin{itemize} + \item $n=1$: The polynomial $x + b_0$ has the root $-b_0$. By assumtion, it has to have a negative real part, so $b_0 > 0$. + + \item $n=2$: The polynomial $x^2+b_1x+b_0=(x-\lambda_1)(x-\lambda_2)$ has the roots $\lambda_1$ and $\lambda_2$, which have a negative real part. Then $b_0 = \lambda_1\lambda_2$ and $b_1 = -\lambda_1-\lambda_2$. Obviously $b_1 > 0$. If $\lambda_1$ and $\lambda_2$ are real, then they are negative and $b_0>0$. Otherwise, they are of the form $\mu\pm i\omega$. In this case, $b_0 = (\mu+i\omega)(\mu-i\omega) = \mu^2+\omega^2 > 0$. + + \item For higher degree, find the decomposition of the polynomial to irreducible factors, which leads to linear and quadratic polynomials. Then each coefficient of the factors is positive. Multiplying those factors together, we get positive coefficients of the whole polynomial. + \end{itemize} +\end{proof} + +\subsection{Stability of equilibria} + +Let the following general differential equation be given: +$$\dot x(t)=f(x(t)),$$ +where $f \in C^1(U)$. For $p\in U$ and $ t\mapsto \phi(t,p)$ denote the solution for which $x(0)=p$ holds (on a maximal time interval $I(p)$). + +\begin{defin} + We say that $p\in U$ is an equilibrium if $f(p) = 0$. In this case, $\phi(t,p)$ is constant over time. So $\phi_t(p)=p$, meaning that $p$ is a fixed point of the flow for all $t \in \R$. +\end{defin} + +\begin{defin} + An equilibrium $p$ is Lyapunov stable if for all $\epsilon > 0$ there is a $\delta > 0$ such that $|q-p| < \delta$ implies $|\phi(t,q)-p| < \epsilon$ for all $t\geq 0$. Otherwise $p$ is called unstable. +\end{defin} + +\begin{defin} + An equilibrium is called attracting if there is a neighborhood $U_0 \subseteq U$ of $p$ such that $\lim_{t\to\infty} \phi(t,q)=p$ for all $q\in U_0$. +\end{defin} + +\begin{defin} + An equilibrium is said to be asymptotically stable if it is Lyapunov stable and attracting. +\end{defin} + +\begin{exam}[An attracting equilibrium that is not Lyapunov stable] + Let the following system be given in polar coordinates + $$\begin{array}{ll}\dot r=r(1-r), &\quad r\geq 0,\\ + \dot \theta=\sin^2\left(\half\theta\right), &\quad (0\leq \theta < 2\pi).\end{array}$$ + + \begin{tikzpicture} + \begin{polaraxis}[ + ymax = 1.5, + ] + + \addplot3[ + samples=12, + samples y=12, + quiver = { + u = {deg(sin(atan2(y,x)/2)^2)},%{veclen(y,x)*(1-veclen(y,x))}, + v = {veclen(y,x)*(1-veclen(y,x))},%{sin(atan2(y,x)/2)^2}, + scale arrows = 0.5, + }, + -latex, + domain=-1.5:1.5, + domain y=-1.5:1.5, + data cs=cart + ] (x, y, 0); + \end{polaraxis} + \end{tikzpicture} + + The point $(r^*,\theta^*) = (1,0)$ is not Lyaponov stable, but attracts $\R^2\setminus \{0\}$. In the polar form it attracts all points with $r > 0$ and $0\leq \theta < 2\pi$. +\end{exam} + +\begin{exam} + Given + $$\begin{array}{rcl}\dot x &=& -y-x^3\\ + \dot y &=& x-y^3.\end{array}$$ + Let $V(x,y):= x^2+y^2, \R^2\to\R$. Taking the derivative with respect to $t$ gives us + $$\frac{d}{dt}V(x,y) = \nabla V(x,y)\cdot\vectwo{\dot x}{\dot y} = 2(x\dot x+y\dot y) = 2(x(-y-x^3)+ y(x-y^3)) = -2(x^4+y^4) < 0.$$ +\end{exam} + +In general, $V \in C^1(\Rn,\R)$. When differentiating with respect to $t$ and setting $t=0$ we get +$$\frac{d}{dt} V(x)|_{t=0} = \nabla V(x)\cdot \dot x|_{t=0} = \nabla V(x)\cdot f(x)|_{t=0}.$$ +So +$$\dot V(x) := \nabla Vf(x) := \nabla V(x)\cdot f(x), \dot V: U\to \R$$ +is the derivative of $V$ with respect to $f$. + +\begin{defin} + Let $p$ be an equilibrium and $U_0 \subseteq U$ an open neighbourhood of $p$. A function $V: U_0\to \R$ is called a Lyapunov function for $p$ if: + \begin{enumerate} + \item $V(p) = 0$ and $V(x) > 0$ for $x \in U_0\setminus\{p\}$. + + \item $V$ is continuous in $U_0$, $C^1$ in $U_0\setminus \{p\}$ and $\dot V(x)\leq 0$ for $x \in U_0\setminus \{p\}$. + \end{enumerate} + If $\dot V(x) < 0$ for all $x\in U_0\setminus\{p\}$, then we call it a strict Lyapunov function for $p$. +\end{defin} + +We can imagine that each orbit moves along $V$ such that the value of $V$ doesn't increase. So as long as the orbit starts close at $p$, it stays close to it. + +\begin{hw} + Consider + $$\dot x = f(x)$$ + in $\R$ with an equilibrium $f(p)=0$. Show that $p$ is asymptotically stable if and only if $V(x) = |x-p|$ is a strict Lyapunov function for $p$ in a neighborhood. +\end{hw} + +\begin{hw} + Pendulum with friction: Given + $$\begin{aligned}\dot x&=y\\ + \dot y &= \sin x-\delta y\end{aligned}$$ + where $\delta \geq 0$. Show that + $$V(x,y) := \half{y^2}-\cos x$$ + is a Lyapunov function at the origin. +\end{hw} + +\begin{hw} + For which $A\in\R^{n\times n}$ is the origin of $\dot x = Ax$ Lyapunov stable? +\end{hw} + +\begin{thm}[Lyapunov, 1892] + The following statements hold: + \begin{enumerate} + \item If there is a Lyapunov function for the equilibrium $p$ then $p$ is Lyapunov stable. + + \item If there is a strict Lyaponov function for the equilibrium $p$ then $p$ is asymptotically stable. + \end{enumerate} +\end{thm} + +\begin{proof} + For the proof, we use some $\epsilon$-$\delta$-tricks. + \begin{enumerate} + \item Let $\epsilon > 0$ such that + $$\overline{B_\epsilon(p)} \subseteq U_0.$$ + Let + $$\alpha := \min_{|x-p|=\epsilon}V(x) > 0.$$ + Clearly, $V(p)<\alpha$. Let $\delta > 0$ such that $|x-p|<\delta$ implies $V(x) < \alpha$ (recall $V$ is continuous).\\ + Then for $q$ with $|q-p| < \delta$ we have $V(\varphi(t,q))< \alpha$ for $t \geq 0$. This is, because $V(\varphi(0,q)) = V(q) < \alpha$ and $\dot V \leq 0$. So the flow will never intersect the sphere $\{x\in\Rn:|x-p| = \epsilon\}$. Therefore we get $|\varphi(t,q)-p|<\epsilon$ for $t\geq 0$. + + \item We show that $\lim_{t\to\infty}\varphi(t,q) = p$ if $|q-p|<\delta$. Since $t\mapsto V(\varphi(t,q))$ is monotone decreasing, the following limit exists: + $$\lim_{t\to\infty}V(\varphi(t,q))=:c \geq 0.$$ + \begin{itemize} + \item If $c = 0$, then the orbit stays in a compact neighborhood of $p$, since $V$ is Lyapunov stable. Therefore the orbit accumulates at a certain point $r$. Since $c = 0$, the only accumulation point possible is $p$. So $\lim_{t\to\infty} \varphi(t,q) = p$. + + \item If $c > 0$ then there is a $\gamma > 0$ such that $|\varphi(t,q)-p|\geq \gamma$ for $t\geq 0$. On the compact set + $$\{x\in U_0: \gamma \leq |x-p|\leq \epsilon\},$$ + we get that + $$\dot V(x)\leq -\beta < 0$$ + for every $x$. Therefore $V(\varphi(t,q))\to-\infty$ as $t\to\infty$, which is a contradiction. + \end{itemize} + \end{enumerate} +\end{proof} + +\begin{hw} + Given the following scalar ODE: + $$\dot x = x^3 \sin^2\left(\reci x\right)$$ + Is the origin Lyapunov stable? Can you find a Lyapunov function? +\end{hw} + +\begin{hw} + Prove the following statements about the pendulum with friction: + \begin{itemize} + \item If $\delta = 0$ then the origin is Lyapunov stable. + + \item If $\delta > 0$ then the origin is asymptotically stable. + \end{itemize} +\end{hw} + +\begin{hw} + Is the following statement true or false? Give a proof or a counterexample. + \begin{itemize} + \item If $V:\R^n\to\R$ is a strict Lyapunov function for the equilibrium $p$, then $\lim_{t\to\infty} \varphi(t,q) = p$ for all $q \in\R^n$.\\ + \end{itemize} +\end{hw} + +\begin{hw} + Lorenz:\\ + Given the following system of equations: + $$\begin{array}{rcl}\dot x&=&\sigma(y-x)\\ + \dot y &=& \rho x-y-xz\\ + z &=& xy-\beta z\end{array}$$ + Show that the origin is globally asymptotically stable if $0<\rho < 1$.\\ + Hint: $V(x,y,z) = \rho x^2+\sigma y^2+\sigma z^2$ +\end{hw} + +Given +$$\dot x(t)=f(x(t))$$ +where $f \in C^1(U)$ and $f(p) = 0$. Then +$$f(x)=f'(p)(x-p)+r(x)$$ +where $f'$ is the Jacobin matrix of $f$. +$$f'=\matthree{\partial_1f_1}{\dots}{\partial_nf_1}{\vdots}{}{\vdots}{\partial_1f_n}{\dots}{\partial_nf_n}=(\partial_jf_i)_{i,j=1}^n$$ +Also $r(p) = 0$ and $\lim_{x\to\infty}\frac{r(x)}{|x-p|}=0$. Let $A := f'(p)$. +\begin{thm} + If $A$ is stable then $p$ is asymptotically stable for $\dot x=f(x)$. +\end{thm} + +\begin{proof} + Assume without loss of generality that $p=0$. Let $Q = Q^T > 0$ such that $QA+A^TQ<0$.\\ + We claim that $V(x)=x^TQx$ is a strict Lyapunov function for $p$. So we need to show that $\dot V(x) < 0$ for $x \neq p$.\\ + $$\dot V(x) = \nabla V(x)\cdot f(x)=2x^TQ (Ax+r(x))$$ + Because $x^TQAx$ is a scalar, we can transpose it, to get to $x^TA^TQx$. Then we get + $$\dot V(x) = x^T(QA+A^TQ)x + 2x^T Q r(x).$$ + We define the inner product + $$\jbr{x,y}:=x^TQy$$ + with the induced norm + $$\|x\|^2 := \jbr{x,x}=x^TQx.$$ + Now let's calculate the following quotient: + $$\frac{\dot V(x)}{V(x)}=\frac{x^T(QA+A^TQ)x}{x^TQx}+2\frac{\jbr{x,r(x)}}{\|x\|^2}$$ + The first term is smaller than or equal $-c$ for $c := \min_{\|x\|=1}\left(\frac{-x^T(QA+A^TQ)x}{x^TQx}\right)>0$. For the second term: + $$\frac{\jbr{x,r(x)}}{\|x\|^2}\leq \frac{\|x\|\|r(x)\|}{\|x\|^2} = \frac{\|r(x)\|}{\|x\|} \to 0$$ + as $x \to 0$. Therefore, $\frac{\dot{V}}{V}$ is negative in a neighborhood of the origin. So for $x \neq 0$ close to $p$, $\dot V(x) < 0$ so $V$ is a Lyapunov function. +\end{proof} + +\begin{hw} + Show that the origin is asymptotically stable for the pendulum with friction $(\delta > 0)$ (linearize). +\end{hw} + +\begin{defin} + An equilibrium $p$ is hyperbolic if $f'(p) \in \R^{n\times n}$ has no eigenvalue with zero real part. +\end{defin} + +\begin{thm}[Hartman-Grobman] + If $f$ is $C^1$ and $p$ is a hyperbolic equilibrium then the local flow $\varphi_t$ is topologically conjugate to the local flow of + $$\dot y = f'(p)y$$ + at the origin. (There is an open neighborhood $U_0$ of $p$, an open neighborhood $U_1$ of $0 \in \R^n$ and a homeomorphism $h:U_0 \to U_1$ such that + $$h\circ \varphi_t = e^{At}\circ h$$ + (here $A := f'(p)$) where this is defined ($\varphi_t(x) \in U_0$).)\\ + (Simon, Perko, Teschl) +\end{thm} + +\begin{defin} + Let $p$ be an equilibrium and $A = f'(p)$. + + \begin{itemize} + \item We say that $p$ is a sink if $\Re(\lambda) < 0$ for all $\lambda \in \sigma(A)$. + + \item We say that $p$ is a source if $\Re(\lambda)>0$ for all $\lambda \in \sigma(A)$. + + \item We say that $p$ is a saddle if it is hyperbolic, meaning th there is a $\lambda_1 \in \sigma(A)$ with $\Re(\lambda_1)<0$ and $\lambda_2 \in \sigma(A)$ with $\Re(\lambda_2)> 0$. + \end{itemize} +\end{defin} + +\begin{hw} + Classify all of the equilibria of + $$\begin{aligned}\dot x&=x^2-y^2-1\\ + \dot y &= 2y.\end{aligned}$$ +\end{hw} + +\begin{exam} + Show that the flows of + $$\begin{aligned}\dot x &= -x\\ + \dot y &= y+x^2\end{aligned}$$ + and + $$\begin{aligned}\dot u &= -u\\ + \dot v &= v\end{aligned}$$ + are topologically conjugate (not only locally, but even globally).\\ + Let + $$h:(x,y)\mapsto (x,y+\frac{x^2}{3}).$$ + Then + $$h^{-1}: (u,v)\mapsto (u,v-\frac{u^2}{3})$$ and $h$ is a homeomorphism. Let + $$(u,v) = h(x,y)$$ + or + $$\begin{aligned}u&=x\\ + v&=y+\frac{x^2}{3}\end{aligned}.$$ + Then + $$\begin{aligned}\dot u &= \dot x=-x = -u\\ + \dot v &= \dot y + \frac{2}{3}x\dot x=y+x^2+\frac{2}{3}(-x^2)= y+\frac{x^2}{3}=v.\end{aligned}$$ +\end{exam} + +\subsection{Polar coordinates} + +If there is a system in Cartesian form like +$$\begin{aligned}\dot x &= f(x,y)\\ +\dot y &= g(x,y)\end{aligned}$$ +we can get to a system in polar form like +$$\begin{aligned}\dot r = F(r,\theta)\\ +\dot \theta = G(r,\theta)\end{aligned}$$ +where +$$\begin{aligned}&x = r\cos(\theta), &y = r\sin(\theta)\\ +&r = \sqrt{x^2+y^2}, &\theta = \arctan(y/x).\end{aligned}$$ +Using some derivative tricks, we get +$$\dot x = \dot r \cos(\theta) +r(-\sin(\theta))\dot \theta, \quad \dot y = \dot r \sin(\theta) + r \cos(\theta) \dot \theta,$$ +$$\dot r = \frac{2x\dot x +2y \dot y}{2\sqrt{x^2+y^2}}, \quad \dot \theta = \frac{\frac{\dot yx - y\dot x}{x^2}}{1+\frac{y^2}{x^2}} = \frac{\dot yx-y\dot x}{x^2+y^2},$$ + +$$\dot x=-y\dot \theta +x\frac{\dot r}{r}, \quad +\dot y = x\dot \theta +y\frac{\dot r}{r},$$ +$$\dot r = \frac{x\dot x + y\dot y}{r}, \quad +\dot \theta = \frac{x\dot y-\dot xy}{r^2}.$$ + +Linearization at a nonhyperbolic equilibrium (these are situations, where the Hartman-Grobman theorem does not apply): + +\begin{exam} + 1D + \begin{itemize} + \item Given + $$\dot x = -x^3,$$ + the equilibrium $0$ attracts from both sides. + + \item Given + $$\dot x = x^3,$$ + the equilibrium $0$ repells. + + \item Given + $$\dot x = x^2,$$ + the flow goes to the right. + + \item Given + $$\dot x = 0,$$ + everything is stationary. (This is the linearization of all three equations above.) + \end{itemize} + +\end{exam} + +\begin{exam} + 2D + \begin{itemize} + \item Given + $$\begin{aligned}\dot r &= -r^3\\ + \dot \theta &= 1\end{aligned}$$ + in polar coordinates or + $$\begin{aligned}\dot x &= -y-xy^2-x^3\\ + \dot y &= x-y^3-x^2y\end{aligned}$$ + in Cartesian coordinates, the flow spirals inwards. So the origin is asymptotically stable. + + \item Given + $$\begin{aligned}\dot r &= r^3\\ + \dot \theta &= 1\end{aligned}$$ + in polar coordinates or + $$\begin{aligned}\dot x &= -y+xy^2-x^3\\ + \dot y &= x+y^3+x^2y\end{aligned}$$ + in Cartesian coordinates, the flow spirals outwards. So the origin is repelling. + + \item Given + $$\begin{aligned}\dot r &= 0\\ + \dot \theta &= 1+r\cos(\theta)\end{aligned}$$ + in polar coordinates or + $$\begin{aligned}\dot x &= -y-xy\\ + \dot y &= x+x^2\end{aligned}$$ + in Cartesian coordinates, we get a center at the origin. + + \item All three examples above have the same linearization: + $$\begin{aligned}\dot x &= -y\\ + \dot y &= x\end{aligned}.$$ + Here the flow moves in circles around the origin. + \end{itemize} +\end{exam} + +\subsection{Asymptotic behavior} + +What do solutions do as $t \to \infty$? Given +$$\dot x(t) = f(x(t))$$ +where $f \in C^1(U, \Rn)$ and $t \mapsto \varphi(t,p)$ is the solution with $x(0) = p$. + +\begin{defin} + For $p \in U$, the $\omega$-limit of $p$ is + $$\omega(p)=\{q\in U: \exists (t_n)_{n\in\N} \subseteq \R \text{ such that } \lim_{n\to\infty}t_n = \infty \text{ and } \lim_{n\to\infty}\varphi(t_n,p)=q\}.$$ + For $p\in U$, the $\alpha$-limit of $p$ is + $$\alpha(p) = \{q\in U:\exists (t_n)_{n\in\N} \subseteq \R \text{ such that }\lim_{n\to\infty}t_n=-\infty \text{ and } \lim_{n\to\infty}\varphi(t_n,p)=q\}.$$ +\end{defin} + +\begin{exam} +Let's do some examples. +\begin{enumerate} + \item Given: + $$\begin{aligned}\dot x&=x\\ + \dot y &= -y.\end{aligned}$$ + \begin{itemize} + \item If $p = 0$ then $\alpha(p) = \{0\}$ and $\omega(p)=\{0\}.$ + + \item If $p \neq 0$ is on the $x$-axis then $\alpha(p)=\{0\}$ and $\omega(p)=\emptyset$. + + \item If $p \neq 0$ is on the $y$-axis then $\alpha(p) = \emptyset$ and $\omega(p) = \{0\}$. + + \item If $p$ is on no axis then $\alpha(p) = \emptyset$ and $\omega(p) = \emptyset$. + \end{itemize} + + \item Given: + $$\begin{aligned}\dot x &= -y+x(1-x^2-y^2)\\ + \dot y &= x+y(1-x^2-y^2)\end{aligned}$$ + or + $$\begin{aligned}\dot r &= r(1-r^2)\\ + \dot \theta &= 1\end{aligned}$$ + + \begin{itemize} + \item If $p = 0$ then $\alpha(p) = \{0\}$ and $\omega(p) = \{0\}$. + + \item If $p \neq 0$ is inside the unit circle then $\alpha(p) = \{0\}$ and $\omega(p)$ is the boundary of the unit circle. + + \item If $|p| = 1$ then $\alpha(p)$ and $\omega(p)$ are the boundary of the unit circle. + + \item If $p$ is outside the unit circle then $\alpha(p)=\emptyset$ and $\omega(p)$ is the boundary of the unit circle. + \end{itemize} + + + + \item Given: + $$\begin{aligned}\dot x &= -y+x(1-x^2-y^2)\\ + \dot y &= x+y(1-x^2-y^2)\\ + \dot z &= \beta > 0 \text{ (constant)} \end{aligned}$$ + Then for every $p \in \R^3$ we get $\alpha(p) = \omega(p) = \emptyset$. + + \item Same as 3, but identify $0$ and $2\pi$ on the $z$-axis. Then the invariant cylinder becomes an invariant torus. If $\beta\in\Q$ then the torus is filled with periodic orbits (and the $\omega$-limit is one of these periodic orbits, provided $p$ is not on the $z$-axis).\\ + If $\beta \notin \Q$ then there are everywhere dense orbits on the torus and $\omega(p)$ is the torus for all $p$ not on the $z$-axis. + + \item Lorenz equation: Strange attractor. +\end{enumerate} +\end{exam} + +\begin{thm} + The following statements are true: + \begin{enumerate} + \item $\omega(p)$ is closed. + + \item $\omega(p)$ is invariant (if $q \in \omega(p)$ then $\varphi(t,q) \in \omega(p)$ for all $t \in \mathbb{R}$). + + \item If $\{\varphi(t,p):t\geq 0\}$ is bounded then $\omega(p)$ is nonempty an connected. + \end{enumerate} +\end{thm} + +\begin{proof} + Let's go through the proof. + \begin{enumerate} + \item Let $q\notin \omega(p)$. Then there is an open neighborhood $U_0\subseteq U$ of $q$ and $T > 0$, such that $\varphi(t,p)\notin U_0$ for all $t \geq T$. So after time $T$, the solution does not enter $U_0$. Therefore $U_0 \subseteq \omega(p)^c$ implying that $\omega(p)^c$ is open and $\omega(p)$ is closed. + + \item Fix $q \in \omega(p)$. Then there is a sequence $(t_n)_{n\in\N} \subseteq \R$, such that $\lim_{n\to\infty}t_n = \infty$ and $\lim_{n\to \infty}\varphi(t_n,p) = q$.\\ + Fix $t\in\R$ and let $\tau_n = t_n+t$. Then $\lim_{n\to\infty}\tau_n=\infty$ and $$\lim_{n\to\infty}\varphi(\tau_n,p) = \lim_{n\to\infty}\varphi(t_n+t,p) = \lim_{n\to\infty}\varphi(t,\varphi(t_n,p))=\varphi(t,q)$$ + (because of the continuous dependence of solutions on the initial conditions). Therefore, we get $\varphi(t,q) \in \omega(p)$. + + \item The solution lies in a compact set $K$. Take any sequence $(t_n)_{n\in\N}\subseteq\R$ such that $\lim_{n\to\infty}t_n=\infty$. Then $(\varphi(t_n,p))_{n\in\N} \subseteq K$ and there is a subsequence $(\varphi(t_{n_k},p))_k$ such that $\lim_{k\to\infty}\varphi(t_{n_k},p) \in K$ exists. Therefore $\omega(p) \neq \emptyset$.\\ + Now we show that $\omega(p)$ is connected. By way of contradiction, assume there exist $G_1, G_2$ open sets such that: + \begin{itemize} + \item $G_1$ and $G_2$ are disjoint. + + \item $G_1 \cup G_2 \supseteq \omega(p)$. + + \item $G_1 \cap \omega(p) \neq \emptyset$ and $G_2 \cap \omega(p) \neq \emptyset$. + \end{itemize} + + Then there are sequences $(t_n)_{n\in\N}, (\tau_n)_{n\in\N} \subseteq \R$ such that + $\lim_{n\to\infty} t_n=\infty$, $\lim_{n\to\infty}\tau_n=\infty$, + $$\lim_{n\to\infty}\varphi(t_n,p)=q_1 \in G_1 \cap \omega(p)$$ + and + $$\lim_{n\to\infty}\varphi(\tau_n,p)=q_2 \in G_2 \cap \omega(p),$$ + where $t_1 < \tau_1 < t_2 < \tau_2 < \dots$.\\ + Let $\theta_n$ be in the interval $(t_n,\tau_n)$ such that $\varphi(\theta_n,p)\notin G_1 \cup G_2$. Then as above $(\varphi(\theta_n,p))_{n\in\N}$ has a convergent subsequence, thus we found a point in $\omega(p) \setminus(G_1 \cup G_2)$ which is a contradiction. + \end{enumerate} +\end{proof} + +\begin{hw} + Sketch a 2D example with nonempty and disconnected $\omega$-limit set. +\end{hw} + +In a one-dimensional system the $\omega$-limit of a point $p$ is either $\emptyset$ or $\{q\}$, where $q$ is an equilibrium. What happens in the two-dimensional case? + +\begin{thm}[Poincar\'e-Bendixson] + Let $U \subseteq \R^2$ be open. Let + $$\dot x(t)=f(x(t))$$ + be given where $f\in C^1(U,\R^2)$. Let $K \subseteq U$ be a forward invariant ($p \in K$ implies $\varphi(t,p)\in K$ for all $t \geq 0$), compact set with finitely many equilibria. Then for any $p \in K$ the set $\omega(p)$ is one of the following: + \begin{itemize} + \item $\omega(p) = \{q\}$, where $q$ is an equilibrium. + + \item $\omega(p) = \gamma$, where $\gamma$ is a closed orbit (the image of a periodic solution). + + \item $\omega(p)$ is the union of $\{q_1, \dots ,q_n\}$ and countably many non closed orbits $\gamma$ such that $\alpha(\gamma) = q_i$ and $\omega(\gamma)=q_j$. + \end{itemize} +\end{thm} + +\begin{defin} + If $q$ is an equilibrium and $\gamma$ is an orbit with $\lim_{t \to \pm\infty}\gamma(t) = q$, then $\gamma$ is called a homoclinic orbit. +\end{defin} + +\begin{defin} + If $q_1, q_2$ are two different equilibria and $\gamma$ is an orbit with $\lim_{t\to-\infty}\gamma(t) = q_1$ and $\lim_{t\to\infty}\gamma(t) = q_2$, then $\gamma$ is called a heteroclinic orbit. +\end{defin} + +\begin{exam} + The system + $$\begin{aligned}\dot x &= x(1-x)(x-y)\\ + \dot y &= y(1-y)(2x-1)\end{aligned}$$ + has an attractin rectangle. +\end{exam} + +\begin{rem} + The Poincar\'e-Bendixson-Theorem does not apply to 2D manifolds other than subsets of $\R^2$ or the $2$-sphere. +\end{rem} + +For instance, let +$$\dot x = v$$ +for $v \in \R^2$ such that $\frac{v_1}{v_2}\notin \Q$ in the $2$-torus $\mathbb{T}^2$. +$$x(t)=tv+p$$ +is dense in $\mathbb{T}^2$ and $\omega(p) = \mathbb{T}^2$. + +\begin{defin} + Given + $$\begin{aligned} + \dot x_1 = f_1(x)\\ + \dot x_2 = f_2(x)\\ + \vdots\\ + \dot x_n = f_n(x) + \end{aligned}$$ + for $f = (f_1, \dots, f_n) \in C(U)$. For $i \in \jbr{n}$, we define $\{x \in U: f_i(x) = 0\}$ the $x_i$-nullcline. +\end{defin} + +\paragraph{Chlorine dioxide-Iodine-Malonic-Acid reaction: $(X = I, Y = ClO_2^-)$} +Given +$$\begin{aligned} \dot x &= a-x-\frac{4xy}{x^2+1}\\ +\dot y &= bx\left(1-\frac{y}{x^2+1}\right),\end{aligned}$$ +where $a,b > 0$ and $x,y\geq 0$. We first compute the nullclines. +$$\begin{aligned}\dot x = 0 &\Leftrightarrow y = \frac{(a-x)(x^2+1)}{4x}\\ +\dot y = 0 &\Leftrightarrow y = x^2+1\end{aligned}$$ +Solving this system of equation gives +$$x^* = \frac a5,\quad y^* = 1+(x^*)^2.$$ +Now we compute the Jacobian matrix $J$ at $(x^*,y^*)$. +$$J (x^*,y^*) = \reci{(x^*)^2+1}\mattwo{3(x^*)^2-5}{-4x^*}{2b(x^*)^2}{-bx^*}$$ +To get information about the eigenvalues, we calculate the determinant and the trace of it. +$$\det J(x^*,y^*)=\frac{5bx^*}{(x^*)^2+1}>0$$ +$$\tr J(x^*,y^*)=\frac{3(x^*)^2-bx^*-5}{(x^*)^2+1}$$ +$$\sgn(\tr J(x^*,y^*)) = \sgn(3a^2-5ab-125)$$ +\begin{itemize} + \item For $b > \frac35a-\frac{25}a$ it is asymptotically stable. + + \item For $b < \frac35a-\frac{25}a$ it is repelling, and, by the Poincar\'e-Bendixson Theorem, there is a closed orbit. + + \item At $b = \frac35a-\frac{25}a$ a supercritical Andronov--Hopf bifurcation occurs (such a bifurcation will be discussed on May 8th). +\end{itemize} + +\begin{defin} + A limit cycle is a closed orbit $\gamma$ which is the $\omega$-limit or $\alpha$-limit of at least one point outside $\gamma$. +\end{defin} + +\begin{defin} + A periodic attractor is a closed orbit such that for all $p$ in a neighborhood of $\gamma$, we get + $$\omega(p)=\gamma.$$ + (Note: a neighborhood of $\gamma$ in $\R^2$ is an annulus, in $\R^n$ it is a torus.) +\end{defin} + +\begin{hw} + Given + $$\begin{aligned} + \dot x &= y+xh(r)\\ + \dot y &= x+yh(r)\\ + r &= \sqrt{x^2+y^2}, + \end{aligned}$$ + write in polar coordinates and find $h$ such that there are infinitely many limit cycles. +\end{hw} + +\begin{thm}[Green's theorem] + Let $F:\R^2\to\R^2$ be smooth, $D\subseteq \R^2$ be a simply connected region, $\gamma$ be its boundary and + $n: \gamma \to\R^2$ is the outward facing unit normal vector field. Then + $$\int_\gamma F\cdot n=\iint_D\divg F.$$ + With $F=(P,Q)$ this reads as + $$\oint_\gamma Pdy-Qdx = \iint_D\partial_x P+\partial_y Q.$$ + +\end{thm} + +\begin{thm}[Bendixson-Dulac criterion] + Given + $$\begin{aligned} + \dot x = f(x,y)\\ + \dot y = g(x,y) + \end{aligned}$$ + where $(f,g):D \to\R^2$ is $C^1$ and $D \subseteq \R^2$ is a simply connected region.\\ + If there is an $h:\R^2\to\R$ which is $C^1$ such that $\text{div}(hf,hg) > 0$ in $D$ (or $\text{div}(hf,hg)<0$ in $D$) then there is no closed orbit that lies entirely in $D$. +\end{thm} + +\begin{proof} + Suppose by contradiction that there is a closed orbit $\gamma$ (with period $T$) with $\gamma(t) = (x(t),y(t))$. Then + $$0 < \iint_{\text{int} \gamma} \text{div}(hf,hg) \stackrel{\text{Green}}{=} \oint_\gamma hfdy-hgdx = \int_0^T (hf\dot y-hg\dot x)dt = \int_0^T (hfg-hgf)dt = 0$$ + which is a contradiction. +\end{proof} + +\begin{hw} + Rule out closed orbits. + \begin{enumerate} + \item Given + $$\begin{aligned} + \dot x &= y\\ + \dot y &= -\sin(x)-\delta y + \end{aligned}$$ + where $\delta > 0$ and $(x,y)\in\R^2$. + + \item Given + $$\begin{aligned} + \dot x &= x(1-x)(x-y)\\ + \dot y &= y(1-y)(2x-1) + \end{aligned}$$ + where $(x,y) \in (0,1)^2$. + + \item The intraspecific competition is decribed by + $$\begin{aligned} + \dot x &= x(n-ax+by)\\ + \dot y &= y(s+cx-dy) + \end{aligned}$$ + where $a,d > 0$ and $(x,y)\in\R_+^2$. + + \item Given + $$\ddot x + p(x)\dot x+q(x)=0$$ + where $p(x) > 0$ for all $x \in \R$. + \end{enumerate} +\end{hw} + +\paragraph{Hilbert's 16th problem:} +Given +$$\begin{aligned} + \dot x = f(x,y)\\ + \dot y = g(x,y) +\end{aligned}$$ +where $f,g$ are polynomials of degree $n$. For a fixed $n$, find the maximum number of limit cycles, and denote this as $H(n)$. It is known that any fixed planar polynomial ODE has only finitely many limit cycles. However, it still not known whether $H(2)$ is finite. It is known that $H(2) \geq 4$, and in fact, people conjecture that $H(2)=4$. Further, there is a cubic example with 13 limit cycles, and hence we know that $H(3)\geq 13$. + +\subsection{LaSalle's invariance principle} + +Given +$$\dot x = f(x),$$ +where $f \in C^1(U, \Rn)$. + +\begin{lem} + Let $V \in C(U,\R)$ such that $V(\varphi(\cdot, p))$ is monotone increasing (or decreasing). Then $V$ is constant on $\omega(p)$. + \label{Constant on orbit} +\end{lem} + +\begin{proof} + Let $q,r \in \omega(p)$. Then there are sequences $(t_n)_{n\in\N}\subseteq \R$ and $(\tau_n)_{n\in\N} \subseteq \R$ such that $\lim_{n\to\infty} t_n = \infty, \lim_{n\to\infty}\tau_n = \infty, \limn \varphi(t_n,p)=q$ and $ \limn \varphi(\tau_n,p)=r$. By refining the sequences, we may assume that $t_n \leq \tau_n \leq t_{n+1}$ for every $n$. Hence, + $$V(\varphi(t_n,p)) \leq V(\varphi(\tau_n,p)) \leq V(\varphi(t_{n+1},p))$$ + for every $n$. Letting $n$ approach $\infty$, we get $V(q) \leq V(r) \leq V(q)$. So $V(r)=V(q)$, showing that $V$ is constant on $\omega(p)$. +\end{proof} + +\begin{thm} + Let $V \in C^1(U,\R)$ such that $\nabla Vf(x)\leq 0$ for all $x \in U$ (or $\geq 0$). Then + $$\omega(p)\subseteq \{x\in U:\nabla Vf(x)=0\}$$ + for all $p \in U$. Moreover, $\omega(p)$ is contained in the maximal invariant subset of $\{x\in U:\nabla Vf(x)=0\}$. +\end{thm} + +\begin{proof} + Suppose $q \in \omega(p)$. Then $\varphi(t,q) \in \omega(p)$ for all $t \geq 0$. By assumtion, the map $t \mapsto V(\varphi(t,q))$ monotone decreasing. By lemma \ref{Constant on orbit} it is constant. By differentiating with respect to time, we get + $$\nabla V(\varphi(t,q))\partial_t\varphi(t,q) = 0.$$ + Because $\dot x = f(x)$, we get + $$\nabla V(\varphi(t,q))f(\varphi(t,q)) = 0$$ + and setting $t=0$, we get $\nabla Vf(q)=0$. +\end{proof} + +\begin{rem} + Such a function is called a Lyapunov function. ($\nabla Vf \leq 0$ or $\nabla Vf \geq 0$.) +\end{rem} + +\begin{thm} + If $V:\Rn \to \R$ is a strict Lyapunov function for the equilibrium $p$ and $V$ is radially unbounded (meaning $V(x) \to \infty$ if $|x| \to \infty$; hence, the sublevelsets of $V$ are bounded) then $\limn\varphi(t,q) = p$ for all $q \in \Rn$ (i.e., $p$ is globally asymptotically stable). +\end{thm} + +\begin{exam}[Pendulum with friction] + Given + $$\begin{aligned} + \dot x &= y\\ + \dot y &= -\sin(x)-\delta y + \end{aligned}$$ + where $\delta > 0$. We define $V(x,y) = \half {y^2}-\cos(x)$ to be our candidate. Then + $$\nabla Vf(x,y) = \sin(x)\cdot y + y(-\sin(x)-\delta y)=-\delta y^2 \leq 0.$$ + So + $$\{(x,y)\in\R^2:\nabla Vf(x,y)=0\} = x-\text{axis}.$$ + The maximal invariant subset of it is $\{(\xi \pi,0), \xi \in \Z\}$. Therefore every bounded solution converges to a point here. +\end{exam} + +\begin{exam} + Given + $$\begin{aligned} + \dot x&= x\\ + \dot y &= -y, + \end{aligned}$$ + we choose $V(x,y) = x^2-y^2$ as our candidate. Then + $$\dot V(x,y) = 2x\dot x-2y\dot y = 2(x^2+y^2) \geq 0.$$ So $\dot V(x,y) = 0$ if and only if $(x,y)=0$. Hence, $\omega(p) = \{(0,0)\}$ or $\omega = \emptyset$. The former holds if $p$ is on the $y-$axis, while the latter holds when $p$ is outside the $y$-axis. +\end{exam} + +\subsection{Hamiltonian systems in 2D} + +Let $U \subseteq R^2$ be open, $H \in C^2(U, \R)$. We analyze systems of the form +$$\begin{aligned} + \dot x &= \partial_y H\\ + \dot y &= -\partial_x H. +\end{aligned}\quad (H)$$ + +\begin{thm}[Conservation of energy] + $H$ is constant along trajectories. +\end{thm} + +\begin{proof} + We just need to show that the time derivative vanishes. + $$\frac{d}{dt} H(x(t),y(t)) = \partial_x H\dot x +\partial_y H \dot y = \partial_x H \partial_y H +\partial_y H (-\partial_x H)=0$$ +\end{proof} + +\begin{rem} + Equilibria of $H$ are exactly the critical points of $H$ (where the gradient of $H$ vanishes). +\end{rem} + +\begin{defin} + An equilibrium $p$ of $\dot x = f(x)$ in $\Rn$ is said to be degenerate if $0 \in \sigma(f'(p))$. Otherwise, it is called non-degenerate. +\end{defin} + +\begin{rem} + For $n = 2$, a non-degenerate equilibrium is either hyperbolic or a center of the linearized system. +\end{rem} + +\begin{defin} + An equilibrium $p$ of $\dot x = f(x)$ on $\R^2$ is called + \begin{itemize} + \item a center if all nearby orbits are closed. + + \item a saddle if there are trajectories $\Gamma_1, \Gamma_2$ that approach $p$ as $t\to\infty$, $\Gamma_3, \Gamma_4$ that approach $p$ as $t\to-\infty$ and there is a $\delta>0$ such that all other trajectories in $B_\delta(p)\setminus\{p\}$ leave $B_\delta(p)$ as $t \to \pm\infty$. + \end{itemize} +\end{defin} + +\begin{thm} + Any non-degenerate equilibrium of $(H)$ is either a saddle (when $p$ is saddle of $H$) or a center (if $p$ is a local extremum of $H$). +\end{thm} + +\begin{proof} + Without loss of generality the equilibrium is at the origin. The linearization is $\vectwo{\dot x}{\dot y}=A\vectwo xy$, where + $$A = \mattwo{\partial_x\partial_y H}{\partial_y^2H}{-\partial_x^2H}{-\partial_y\partial_x H}.$$ + Then $\tr A = 0$ and $\det A= -(\partial_x\partial_yH)^2+\partial_y^2 H\partial_x^2 H$. The Hessian $\mathcal H$ of $H$ is + $$\mathcal H = \mattwo{\partial_x^2H}{\partial_x\partial_y H}{\partial_x\partial_yH}{\partial_y^2H}$$ + Then $\det \mathcal H = \det A$. Since the equilibrium is non-degenerate, we have $\det\mathcal H \neq 0$. Then we get two cases. + \begin{enumerate} + \item In the first case, we have $\det \mathcal H < 0$ ($\mathcal H$ is indefinite). Therefore it's a saddle of $H$ and a saddle of the linearized system. So the equilibrium is a saddle. + + \item In the other case, we have $\det \mathcal H > 0$ ($\mathcal H$ is positive or negative definite). Therefore it's a strict local extremum of $H$. Then the level sets are closed curves. Since $H$ is constant along solutions, the equilibrium is a center. + \end{enumerate} + +\end{proof} + +\subsection{Special Hamiltonian systems: Newtonian systems} + +Given +$$\ddot x = F(x)$$ +in $\R$ (scalar ODE, second order). We can use the substitution $y:= \dot x$ to get two ODEs of order one + + +$$\begin{aligned} + \dot x &= y\\ + \dot y &= F(x). +\end{aligned}\quad (N)$$ +(planar ODE, first order). Now let +$$H(x,y) = \half{y^2}-\int_{x_0}^x F(s)ds$$ +In this case, $H(x,y)$ is called the total energy and $\half{y^2}$ is the kinetic energy. The rest is the potential energy, so +$$H(x,y) = T(y)+U(x).$$ + +\begin{thm} + The following statements hold: + \begin{enumerate} + \item The equilibria of $(N)$ all lie on the $x$-axis. + + \item The point $(x^*,0)$ is an equilibrium of $(N)$ if and only if $x^*$ is a critical point of $U$ ($\Leftrightarrow$ $F(x^*) = 0$). + + \item If $x^*$ is a strict local max/min of $U$ then $(x^*,0)$ is a saddle/center of $(N)$. + + \item The phase portrait of $(N)$ is symmetric to the $x$-axis. + \end{enumerate} +\end{thm} + +\begin{exam} + Given + $$\ddot x +\sin(x) = 0,$$ + so $F(x) = -\sin(x)$. By substitution, we get + $$\begin{aligned} + \dot x &= y\\ + \dot y &= -\sin(x). + \end{aligned}$$ + The potential energy is + $$U(x) = -\int_0^x-\sin(s)ds = -[\cos(s)]_{s=0}^{s=x} = 1-\cos(x).$$ + Then the total energy is + $$H(x,y) = \half {y^2}+1-\cos(x).$$ + So $H(x,y) = 2$ if and only if $y = \pm\sqrt{2(\cos x+1)}$. We can conclude that $(-\pi,0)$ and $(\pi,0)$ are connected by heteroclinic orbits.\\ + \\ + Equilibria: The point $(0,0)$ is a center (Lyapunov stable), while $(\pm \pi,0)$ are saddles (not Lyapunov stable). +\end{exam} + +\subsection{Gradient systems in $\Rn$} + +Let $V \in C^2(U,\R)$ and +$$\dot x = -\nabla V(x)^T,$$ +where $\nabla V(x) = (\partial_{x_1} V, \dots, \partial_{x_n} V)$. +So +$$\dot x_i = -\partial_{x_i} V, \quad i \in\jbr{n} \text{ for all }$$ +Sometimes the system +$$\dot x = \nabla V(x)^T$$ +is analyzed (but not here). Critical points of $V$ are the points, where $\nabla V(x) = 0$ (and these are exactly the equilibria of the ODE).\\ +Regular points of $V$ are the points, where $\nabla V(x) \neq 0$. In this case $\nabla V(x)$ is orthogonal to the level sets $\{V = c\}$ and the vector field points to the steepest descent. + +\begin{exam} + Let $V(x,y) = \half1(2x^2+y^2)$. + $$\begin{aligned} + \dot x &= -2x\\ + \dot y &= -y. + \end{aligned}$$ + The level sets look like ellipses. The flows are orthogonal to the level sets and converge to the origin. +\end{exam} + +\begin{lem} + For a gradient system, the following statements hold: + \begin{enumerate} + \item $V$ is a Lyapunov function ($\dot V \leq 0$). + + \item $\dot V(p)=0$ if and only if $p$ is an equilibrium. + + \item Strict local minima of $V$ are asymptotically stable equilibria. + + \item The $\omega$-limit set consists of equilibria only. + + \item If equilibria are isolated then every bounded trajectory converges to an equilibrium. + \end{enumerate} +\end{lem} + +\begin{proof} + The statements are simple to prove. + \begin{enumerate} + \item $\dot V = \nabla V\cdot(-\nabla V)^T = -\|\nabla V\|^2 \leq 0$. + + \item We know that $p$ is an equilibrium if and only if $\nabla V(p) = 0$. This is the case if and only if $\dot V(p) = 0$. + + \item Follows from the Lyapunov stability theorem. + + \item Follows from LaSalle. + + \item trivial. + \end{enumerate} +\end{proof} + +\begin{exam} + Let $V(x,y) = (x+1)^2(x-1)^2+y^2$. So + $$\begin{aligned} + \dot x &= -4(x+1)x(x-1)\\ + \dot y &= -2y. + \end{aligned}$$ + Equilibria are: + \begin{itemize} + \item $(-1,0)$ asymptotically stable + + \item $(0,0)$ saddle + + \item $(1,0)$ asymptotically stable + \end{itemize} +\end{exam} + +Linearization at an equilibrium $-(\partial_{x_i}\partial_{x_j}V)_{i,j}^n$ is symmetric. Therefore eigenvalues are real. + +\begin{thm} + A non-degenerate equilibrium of a planar gradient system is either a saddle (when it is a saddle of $V$), a stable node (when it is a strict local minimum of $V$) or an unstable node (when it is a strict local maximum of $V$). +\end{thm} + +\begin{rem} + Surprisingly $\omega(p)$ can be a continuum of equilibria (for example, a circle). +\end{rem} + +How to recognize a gradient system? +The system $\dot x = f(x)$ is a gradient system in $\Rn$ if and only if $\partial_{x_j}f_i = \partial_{x_i}f_j$ for $i,j\in\jbr{n}$. + +\begin{hw} + Given $\dot x=Ax,$ where $ A\in\R^{n\times n}$. Which linear systems are gradient systems? Find $V$. +\end{hw} + +\begin{thm} + Given + $$\begin{aligned} + \dot x &= f(x,y)\\ + \dot y &= g(x,y). + \end{aligned}$$ + Rotate the vector field by $-90$ degree. + $$\begin{aligned} + \dot x &= g(x,y)\\ + \dot y &= -f(x,y) + \end{aligned}$$ + A center of the first system is a node in the second system. A saddle of the first system is a saddle of the second system. Focus refers to focus. At non-equilibrium points, the trajectories are orthogonal. The first one is a Hamiltonian system if and only if the second one is a gradient system. (Flows and level sets switch roles.) +\end{thm} + +\begin{hw} + Given + $$\begin{aligned} + \dot x &= y\\ + \dot y &= -x+x^2. + \end{aligned}$$ + Find the Hamiltonian $H$ and sketch the phase portrait. +\end{hw} + +\subsection{First integral (or constant of motion)} + +Given +$$\dot x(t)=f(x(t)),$$ +where $f \in C^1(U, \Rn)$. + +\begin{defin} + A function $V \in C^1(U,\Rn)$ is called a first integral or a constant of motion if $\dot V = 0$ in $U$. +\end{defin} + +\begin{exam}[Lotka reactions] + Given + $$\begin{array}{rcl} + X &\stackrel{\kappa_1}{\to}& 2X\\ + X+Y &\stackrel{\kappa_2}{\to}& 2Y\\ + Y &\stackrel{\kappa_3}{\to}& 0 + \end{array}$$ + we can model it as a system of differential equations. + $$\begin{array}{rcccl}\dot x &=&\kappa_1x-\kappa_2xy &=& x(\kappa_1-\kappa_2y)\\ + \dot y&=&\kappa_2xy-\kappa_3y &=& y(\kappa_2x-\kappa_3)\\ + &&\kappa_1,\kappa_2, \kappa_3 &>& 0 + \end{array}$$ + The ositive equilibrium is $(x^*,y^*)=\left(\frac{\kappa_3}{\kappa_2},\frac{\kappa_1}{\kappa_2}\right)$. Calculating the Jacobian matrix at $(x^*, y^*)$ gives + $$J = \mattwo0{-\kappa_3}{\kappa_1}0.$$ + So $\sigma(J)=\{\pm\omega i\}$ with $\omega = \sqrt{\kappa_1\kappa_3}$. Now we define + $$V(x,y)=\kappa_3\log x + \kappa_1\log y-\kappa_2(x+y).$$ + Then + $$\dot V(x,y) = \partial_xV\dot x+\partial_y V\dot y = \left(\frac{\kappa_3}{x}-\kappa_2\right)x(\kappa_1-\kappa_2y)+\left(\frac{\kappa_1}{y}-\kappa_2\right)y(\kappa_2x-\kappa_3) = 0,$$ + so $V$ is a first integral. +\end{exam} + +\begin{exam}[Ivanova reactions] + Given + $$\begin{array}{rcl}Z+X &\stackrel{\kappa_1}{\to}& 2X\\ + X+Y &\stackrel{\kappa_2}{\to}& 2Y\\ + Y+Z &\stackrel{\kappa_3}{\to}& 2Y + \end{array}$$ + or + $$\begin{array}{rcl}\dot x &=& x(\kappa_1z - \kappa_2y)\\ + \dot y &=& y(\kappa_2x - \kappa_3z)\\ + \dot z &=& z(\kappa_3y - \kappa_1x),\end{array}$$ + define + $$V_1(x,y,z) = x+y+z.$$ + Then + $$\dot V_1=\dot x+\dot y+\dot z = 0,$$ + so $V_1$ is a first integral. We can get a different first integral defining + $$V_2(x,y,z) = x^{\kappa_3}y^{\kappa_1}z^{\kappa_2} \text{ or } \log x^{\kappa_3}y^{\kappa_1}z^{\kappa_2}.$$ + In those cases + $$\dot V_2=0$$ + and we can conclude that $x(t)^{\kappa_3}y(t)^{\kappa_1}z(t)^{\kappa_2}$ is constant. +\end{exam} + +\begin{defin}[Lotka-Volterra equation] + A Lotka-Volterra equation is a system of equations like + $$\dot x_i = x_i\left(r_i + \sum_{k=1}^na_{ik}x_k\right)$$ + where $i \in \jbr{n}$. +\end{defin} + +\begin{exam}[A Newtonian system] + Given + $$\begin{aligned} + \dot x &= y\\ + \dot y &= -x+x^3 + \end{aligned}$$ + we can find the first integral + $$V(x,y)=\half{y^2}+\half{x^2}-\frac{x^4}{4}$$ + since + $$\dot V(x,y) = (x-x^3)y +y(-x+x^3)=0.$$ +\end{exam} + +\begin{rem} + For a Hamiltonian system + $$\begin{aligned} + \dot x&=\partial_y H\\ + \dot y &= -\partial_x H + \end{aligned}$$ + $H$ is a constant of motion. +\end{rem} + +\begin{rem} + A planar vector field $(f,g)$ is divergence-free if and only if + $$\begin{aligned} + \dot x &= f(x,y)\\ + \dot y &= g(x,y) + \end{aligned}$$ + is Hamiltonian system. Why? + Let $H$ be such that + $$\begin{aligned} + \partial_y H &= f\\ + \partial_x H &= -g. + \end{aligned}$$ + This holds if and only if + $$\partial_y\partial_xH = \partial_x\partial_yH.$$ + Now we rearrange it a bit + $$\partial_xf = -\partial_yg$$ + or + $$\divg(f,g) = \partial_xf+\partial_y g = 0.$$ + How to find $H$? + $$H(x,y) = \int f(x,y)dy+c(x)$$ + where $c(x)$ is found by making sure $-\partial_xH=g$ holds. +\end{rem} + +\begin{hw} + The system + $$\begin{aligned} + \dot x &= -2x-2y-2\\ + \dot y &= -2x+2y-2 + \end{aligned}$$ + is divergence-free. Find the Hamiltonian function $H$. +\end{hw} + +\begin{lem} + Let $f:U\to \Rn$ locally Lipschitz, $v:U\to \R_{>0}$ locally Lipschitz. Then the orbits of $\dot x(t)=f(x(t))$ and $\dot y(t)=v(y(t))f(y(t))$ coincide and the directions of the flows are the same. +\end{lem} + +\begin{exam} + The systems + $$\begin{aligned} + \dot x &= y\\ + \dot y &= -x+x^3 + \end{aligned} + \leftrightarrow + \begin{aligned} + \dot x &= 2y\\ + \dot y &= -2x+2x^3 + \end{aligned} + \leftrightarrow + \begin{aligned} + \dot x &= (x^2+y^2+1)y\\ + \dot y &= (x^2+y^2+1)(-2x+2x^3) + \end{aligned}$$ + have the same orbits. +\end{exam} + +\begin{exam}[Lotka ODE in $\R^2_+$] + For $v(x,y)=\reci{xy}$ let + $$\begin{aligned} + \dot x &= \frac{\kappa_1}{y}-\kappa_2\\ + \dot y &= \kappa_2-\frac{\kappa_3}{x} + \end{aligned}$$ + be given. +\end{exam} + +\begin{hw} + Find the Hamiltonian function $H$. +\end{hw} + +\begin{defin} + For + $$\begin{aligned} + \dot x=f(x,y)\\ + \dot y = g(x,y) + \end{aligned}$$ + the function $v(x,y) > 0$ is called a Dulac function if $\divg(vf,vg) = 0$. +\end{defin} + +\subsection{How to find centers?} + +Given +$$\begin{aligned} + \dot x &= f(x,y)\\ + \dot y &= g(x,y) +\end{aligned}$$ +where $(x^*,y^*)$ is an equilibrium and $J \in \R^{2\times 2}$ is the Jacobian matrix at $(x^*,y^*)$. If $\tr J = 0$ and $\det J > 0$ then $\sigma(J) = \{\pm \omega i\}$ with $\omega = \sqrt{\det J}$. In this case the equilibrium of the linearization is a center. Try to find a Dulac function. + +\subsubsection{Planar S-systems} + +Given +$$\begin{aligned} + \dot x_1 &= \alpha_1 x_1^{g_{11}}x_2^{g_{12}}-\beta_1x_1^{h_{11}}x_2^{h_{12}}\\ + \dot x_2 &= \alpha_2 x_1^{g_{21}}x_2^{g_{22}}-\beta_2x_1^{h_{21}}x_2^{h_{22}} +\end{aligned}$$ +where $\alpha_1, \alpha_2, \beta_1, \beta_2 > 0$ and $g_{ij}, h_{ij} \in \R$ for $i,j = 1,2$. With some nonlinear transformation: +$$\begin{aligned} + \dot u &= e^{a_1u+b_1v}-e^{a_2u+b_2v}\\ + \dot v &= e^{a_3u+b_3v}-e^{a_4u+b_4v} +\end{aligned}$$ +For which $a_i,b_i$ is the origin a center? + +$$J=\mattwo{a_1-a_2}{b_1-b_2}{a_3-a_4}{b_3-b_4}$$ +is the Jacobian at the origin. Assume $\tr J=0$ and $\det J > 0$. Assume further $a_1=a_2$ and $b_3=b_4$. Use the Dulac function $e^{-a_1u-b_4v}$. Then +$$\begin{aligned} + \dot u &= e^{(b_1-b_4)v}-e^{(b_2-b_4)v}\\ + \dot v &= e^{(a_3-a_1)u}-e^{(a_4-a_1)u} +\end{aligned}$$ +is divergence-free and the origin is a center. + +\begin{hw} + Find $H(u,v)$, such that + $$\begin{aligned} + \dot u &= \partial_v H\\ + \dot v &= -\partial_u H. + \end{aligned}$$ +\end{hw} + +\subsubsection{Reversible systems} + +Given +$$\begin{aligned} + \dot x &= f(x,y)\\ + \dot y &= g(x,y). +\end{aligned}$$ +Assume $f$ is odd in $y$ ($f(x,-y) = -f(x,y)$) and $g$ is even in $y$ ($g(x,-y) = g(x,y)$). For example, Newtonian systems. If $(x(t), y(t))$ is a solution, then $(\tilde x(t), \tilde y(t)):=(x(-t),-y(-t))$ is also a solution. We can show this directly. +$$\dot{\tilde x}(t) = -\dot x(-t)=-f(x(-t),y(-t))=-f(\tilde x(t),-\tilde y(t)) = f(\tilde x(t),\tilde y(t))$$ +$$\dot{\tilde y}(t) = \dot y(-t)=g(x(-t),y(-t))=g(\tilde x(t),-\tilde y(t)) = g(\tilde x(t),\tilde y(t))$$ + +\begin{thm} + An equilibrium on the $x$-axis of a reversible system with purely imaginary eigenvalues is a center. +\end{thm} + +More generally: +\begin{itemize} + \item Let $R: \R^2\to \R^2$ be a reflection along a line. + + \item A vector field $F:\R^2\to \R^2$ is said to be reversible with respect to $R$ if $-R^{-1}\circ F\circ R = F$. + + \item A similar theorem holds. +\end{itemize} + +\paragraph{Reversibility with respect to $x = y$ line:} + +Generally, a system of the form +$$\begin{aligned} + \dot x &= f(x,y)\\ + \dot y &= -f(y,x) +\end{aligned}$$ +is reversible with respect to the $x=y$ line. + +\begin{exam} + Given + $$\begin{aligned} + \dot u &= e^{(a_1-a)u+(b_1-b)v}-e^{(a_2-a)u+(b_2-b)v}\\ + \dot v &= e^{(a_3-a)u+(b_3-b)v}-e^{(a_4-a)u+(b_4-b)v} + \end{aligned}$$ + where we assume that + $$\begin{aligned} + a_1-a = b_4-b\\ + a_2-a = b_3-b\\ + a_3-a = b_2-b\\ + a_4-a = b_1-b, + \end{aligned}$$ + the system is reversible with respect to the $u=v$ line. There exist such $a,b$ if and only if $$a_1-b_4=a_2-b_3 = a_3-b_2=a_4-b_1 \quad (*).$$ + Then the origin is thus a center if $(*)$ holds and $\det J > 0$ (notice that $\tr J=0$ follows automatically from $(*)$). +\end{exam} + + + +\begin{hw} + Figure out when + $$\begin{aligned} + \dot u &= f(u,v)\\ + \dot v &= g(u,v) + \end{aligned}$$ + is reversible with respect to + \begin{enumerate} + \item the $v$-axis + + \item the $v=-u$ line. + \end{enumerate} + And try to find planar $S$-systems with a reversible center (especially in the latter case, i.e., reversible with respect to the line $v=-u$). +\end{hw} + +\subsection{Stable and unstable manifolds} + +\begin{exam} + For the system + $$\begin{aligned} + \dot x &= -x\\ + \dot y &= -y+x^2\\ + \dot z &= z+x^2 + \end{aligned}$$ + the only equilibrium is at the origin. The Jacobian matrix at the origin is + $$J = \matdiagthree{-1}{-1}{1}.$$ + $$\begin{aligned} + E^s &= (x,y)-\text{axis}\\ + E^c &= \{0\}\\ + E^u &= z-\text{axis} + \end{aligned}$$ + Solution: + $$\begin{aligned} + x(t) &= x(0)e^{-t}\\ + y(t) &= y(0)e^{-t}+x(0)^2(e^{-t}-e^{-2t})\\ + z(t) &= z(0)e^t+\frac{x(0)^2}{3}(e^t-e^{-2t}) + \end{aligned}$$ + Obeserve that if $z(0) = -\frac{x(0)^2}{3}$ then + $$(x(t),y(t),z(t)) \stackrel{t\to\infty}{\to} (0,0,0)$$ + and if $x(0) = y(0) = 0$ then + $$(x(t),y(t),z(t)) \stackrel{t\to-\infty}{\to} (0,0,0).$$ + Define + $$W^s=\{(x,y,z)\in\R^3:z=-\frac{x^2}{3}\}$$ + the stable manifold (tangent to $E^s$) and + $$W^u=\{(x,y,z)\in\R^3:x=y=0\}$$ + the unstable manifold ($W^u = E^u$). +\end{exam} + +Setting +$$\dot x(t) = f(x(t))$$ +where $f\in C^1(U,\Rn)$. Assume $0\in U$ is a hyperbolic equilibrium ($f(0) = 0$ and $\Re \lambda \neq 0$ for all $\lambda \in \sigma(f'(0))$. Then $\Rn = E^s \oplus E^u$. + +\begin{thm}[Stable and unstable manifolds] + There exist a neighborhood $\tilde U$ of the origin, $\psi\in C^1(E^s\cap\tilde U, E^u)$ and $\phi\in C^1(E^u\cap \tilde U, E^s)$ for which $W^s=\{(x_s,\psi(x_s)): x_s\in E^s\cap \tilde U\}$ is the stable manifold and $W^u=\{(\psi(x_u),x_u),x_u\in E^u \cap \tilde U\}$ is the unstable manifold with + \begin{enumerate} + \item $W^s$ is positively invariant ($\varphi_t(W^s)\subseteq W^s$ for $t \geq 0$). + + $W^u$ is negatively invariant ($\varphi_t(W^u)\subseteq W^u$ for $t \leq 0$). + + \item $W^s$ is tangential to $E^s$ at the origin. $W^u$ is tangential to $E^u$ at the origin. + + \item $\lim_{t\to\infty} \varphi(t,p) = 0$ for $p\in W^s$ and $\lim_{t\to-\infty} \varphi(t,p)=0$ for $p\in W^u$. + \end{enumerate} +\end{thm} + +\begin{rem} + If $f$ is $C^r$ for $r \geq 1$ (or analytic) then $\psi$ and $\phi$ are also $C^r$ (or analytic). +\end{rem} + +\begin{exam} + Given + $$\begin{aligned} + \dot x &= -x\\ + \dot y &= y-x^2. + \end{aligned}$$ + Draw the phase portrait. + We first come to the obvious conclusions + $$\begin{aligned} + E^s = x\text{-axis}\\ + E^u = y\text{-axis} + \end{aligned}$$ + $$\begin{aligned} + W^s &= ?\\ + W^u &= y\text{-axis}. + \end{aligned}$$ + So how do we find $W^s$. We choose the following Ansatz for the stable manifold: + $$y = \psi(x)=a_2x^2+a_3x^3+\dots$$ + It must be tangential to the $x$-axis. So we drop the first two terms $a_0$ and $a_1x$. + $$\dot y = \psi'(x)\dot x$$ + Pluggin it in and using the system from before, we get + $$(a_2-1)x^2+\sum_{k=3}^\infty a_kx^k=\left(\sum_{k=2}^\infty ka_kx^{k-1}\right)(-x).$$ + Comparing coefficients gives us: + $$\begin{aligned} + a_2-1 &=-2a_2\\ + a_k &= -ka_k \text{ for } k \geq 3 + \end{aligned}$$ + Therefore $a_2 = \reci3$ and $a_k = 0$ for $k\geq 3$. +\end{exam} + +\begin{defin}[Global mainfolds] + Global stable manifold: $S = \bigcup_{t \leq 0} \varphi_t(W^s)$\\ + Global unstable manifold: $U=\bigcup_{t\geq 0}\varphi_t(W^u)$. +\end{defin} + +\begin{prop} + The global stable and unstable manifolds are invariant (meaning $\varphi_t(S)\subseteq S$ for all $t \in \mathbb{R}$ and $\varphi_t(U)\subseteq U$ for all $t \in \mathbb{R}$) and + $$\lim_{t\to \infty}\varphi(t,p)=0$$ + for $p \in S$ and + $$\lim_{t\to-\infty}\varphi(t,p) = 0$$ + for $p\in U$. +\end{prop} + +\begin{exam} + The system + $$\begin{aligned} + \dot x &=-x-y^2\\ + \dot y &= y+x^2 + \end{aligned}$$ + is reversible with respect to the line where $x = y$ (since we can swap the roles of $x$ and $y$ without changing the system). + $$J(x,y) = \mattwo{-1}{-2y}{2x}{1}$$ + $$J(0,0)=\matdiagtwo{-1}1$$ + $$J(-1,-1)=\mattwo{-1}{2}{-2}{1}$$ + $S$ and $U$ intersect in a homoclinic loop. +\end{exam} + +\subsection{Center manifold} + +Given +$$\begin{aligned} + \dot x &= xy+x^3\\ + \dot y &= -y-2x^2 +\end{aligned}$$ +we get the Jacobian matrix at the origin +$$J = \matdiagtwo{0}{-1}.$$ +Since $\sigma(J) = \{0,-1\}$ the Jacobian matrix is not hyperbolic and +$$\begin{aligned} + E^s&= y-\text{axis}\\ + E^c&= x-\text{axis}\\ + E^u&= \{0\}. +\end{aligned}$$ + +Setting $x \in \R^c, y \in \R^{s+u}$ where $c+s+u=n$, we get +$$\begin{aligned} + \dot x &= Ax+f(x,y) \text{ with } f(0,0) = 0, f'(0,0)=0\\ + \dot y &= By+g(x,y) \text{ with } g(0,0) = 0, g'(0,0)=0, +\end{aligned}$$ +where $(0,0) \in U$ and $(f,g)\in C^r(U,\Rn)$. The Jacobian matrix at $(0,0)$ is +$$J=\matdiagtwo{A}{B}$$ +Assume $\Re \lambda = 0$ for all $\lambda \in \sigma(A)$ and $\Re \lambda \neq 0$ for all $\lambda \in \sigma(B)$. + +\begin{thm}[Center manifold] + There exists a neighborhood $\tilde U$ of the origin and a function $\psi \in C^r(E^c\cap \tilde U,E^s\oplus E^u)$ for which + \begin{enumerate} + \item $W^c = \{(x,\psi(x)): x\in E^c\cap \tilde U\}$ is locally invariant. + + \item $\psi(0) = 0, \psi'(0) = 0$ (meaning $W^c$ is tangential to $E^c$ at the origin. + + \item $B\psi(x)+g(x,\psi(x)) = \psi'(x)(Ax+f(x,\psi(x)))$ (this helps finding $\psi$) + + \item The system + $$\begin{aligned} + \dot x &= Ax +f(x,\psi(x))\\ + \dot y &= By + \end{aligned}$$ + is locally topologically equivalent to the original system at the origin. (Generalization of the Hartman-Grobman Theorem to the nonhyperbolic case.) + \end{enumerate} +\end{thm} + +\begin{rem} + Differentiating $y(t)=\psi(x(t))$ with respect to the time, one gets 3). +\end{rem} + +\paragraph{Bad news:} +The center manifold is not unique, and need not be as smooth as $(f,g)$. (E.g.\ for analytic $(f,g)$ there can be a continuum of center manifolds, and only one of them is analytic. Or even none of them is analytic!) + +\paragraph{Good news:} +The Taylor series expansion of $\psi$ is unique (as far as it exists), and can usually be computed. All orbits near the origin that stay near the origin for all time $t\in\R$ are contained in every center manifold. + +\begin{exam} + Given + $$\begin{aligned} + \dot x &= xy+x^3\\ + \dot y &= -y-2x^2 + \end{aligned}$$ + approximate the center manifold with the ansatz + $$y=\psi(x)=a_2x^2+a_3x^3+\dots$$ + The linear term is missing, because the center manifold must be tangential to the center subspace. By the invariance of $W^c$, $y=\psi'(x)x$. + $$-\sum_{k=2}^\infty a_kx^k-2x^2=\left(\sum_{k=2}^\infty ka_kx^{k-1}\right)\left(x\sum_{k=2}^\infty a_kx^k+x^3\right)$$ + Comparing the coefficients of $x^2$, we get $$-a_2-2=0$$ + or + $$a_2=-2.$$ + So we conclude that + $$\psi(x)=-2x^2+O(x^3)$$ + and + $$\dot x = x(-2x^2+O(x^3))+x^3=-x^3+O(x^4).$$ + So the trajectories on the center manifold tend to the origin. +\end{exam} + +\begin{exam} + Given + $$\begin{aligned} + \dot x &= x^2y-x^5\\ + \dot y &= -y+x^2, + \end{aligned}$$ + a similar analysis as above reveals + $$y=\psi(x)=x^2+O(x^5)$$ + so + $$\dot x = x^4+O(x^5).$$ + Hence, on any center manifold, the origin attracts for $x<0$ and repels for $x>0$. + +\end{exam} + +\subsection{Andronov--Hopf bifurcation} + +\begin{exam} + Given + $$\begin{aligned} + \dot x &= \alpha x-y-x(x^2+y^2)\\ + \dot y &= x+\alpha y - y(x^2+y^2), + \end{aligned}$$ + where $\alpha \in \R$ is a parameter. + The Jacobian at the origin is + $$\mattwo\alpha{-1}1\alpha$$ + with the eigenvalues $\alpha \pm i$. In polar coordinates, the system is + $$\begin{aligned} + \dot r &= r(\alpha-r^2)\\ + \dot \theta &= 1. + \end{aligned}$$ + \begin{itemize} + \item If $\alpha < 0$: The solutions spiral counter clockwise to the origin. It is linearly stable. It approaches the origin at an exponential speed. + + \item If $\alpha = 0$: The solutions spiral counter clockwise to the origin much slower. + + \item If $\alpha > 0$: We get a stable limit cycle of radius $\sqrt{\alpha}$. + \end{itemize} + Supercritical Andronov--Hopf bifurcation. +\end{exam} + +\begin{exam} + Given + $$\begin{aligned} + \dot x &= \alpha x-y+x(x^2+y^2)\\ + \dot y &= y + \alpha y + y(x^2+y^2) + \end{aligned}$$ + or + $$\begin{aligned} + \dot r &= r(\alpha + r^2)\\ + \dot \theta &= 1. + \end{aligned}$$ + \begin{itemize} + \item If $\alpha < 0$: We get an unstable limit cycle of radius $\sqrt{-\alpha}$. + + \item If $\alpha = 0$: The solutions spiral counter clockwise away from the origin much slower than for $\alpha>0$. + + \item If $\alpha > 0$: The solutions spiral counter clockwise away from the origin. It is linearly stable. It leaves the origin at an exponential speed. + \end{itemize} + Subcritical Andronov--Hopf bifurcation. +\end{exam} + +\begin{exam} + Given + $$\begin{aligned} + \dot x &= \alpha x - y\\ + \dot y &= x+\alpha y + \end{aligned} \quad\text{ or in polar form }\quad\begin{aligned} + \dot r &= \alpha r\\ + \dot \theta &= 1. + \end{aligned}$$ + \begin{itemize} + \item If $\alpha < 0$: The solutions spiral counter clockwise to the origin. It is linearly stable. It approaches the origin at an exponential speed. + + \item If $\alpha = 0$: The origin is a center. + + \item If $\alpha > 0$: The origin repells. + \end{itemize} + Vertical Andronov--Hopf bifurcation. +\end{exam} + +\begin{thm} + Let $U \subseteq \R^2$ be open and + $$\dot x(t) = f_\alpha(x(t))$$ + be a familiy of ODEs, where $\alpha \in (-\epsilon, \epsilon)$ for some $\epsilon > 0$. We assume that + $$(\alpha,x) \mapsto f_\alpha(x)$$ + is $C^1$ with respect to $\alpha$ and $C^3$ with respect to $x$. Assume $f_\alpha(0) = 0$ for all $\alpha \in (-\epsilon, \epsilon)$. Let + $$\mu(\alpha)\pm i\omega(\alpha)$$ + be the eigenvalues of the Jacobian matrix at the origin, + where $\mu(0)=0$ and $\omega(0) > 0$. + Assume $\mu'(0)\neq 0$ (transverality) and $L_1\neq 0$ (nondegeneracy), where $L_1$ is the first focal value (the computation is explained in the next lemma). Then there are invertible coordinate and parameter changes and also time reparametrisation transforming the + $$\dot x(t)=f_\alpha(x(t))$$ + to + $$d_t y(t)=\mattwo{\beta}{-1}{1}{\beta}y\pm|y|^2y+O(|y|^4),$$ where $\pm$ is the sign of $L_1$. Furthermore, omitting $O(|y|^4)$ leads to a family that is locally topologically equivalent near the origin. + \begin{itemize} + \item $L_1<0$: supercritical Andronov--Hopf (stable limit cycle) + + \item $L_1>0$: subcritical Andronov--Hopf (unstable limit cycle) + \end{itemize} +\end{thm} + +\begin{proof} + e.g. Kuznetsov: Elements of bifurcation theory (Section 3.5) +\end{proof} + +\begin{lem} + Given + $$\begin{aligned} + \dot x &= f(x,y)=-\omega y+\sum_{i+j=2} f_{ij}x^iy^j\\ + \dot y &= g(x,y)=\omega x+\sum_{i+j=2} g_{ij}yx^iy^j. + \end{aligned}$$ + We define, $f_{ij}=\frac{1}{i!j!}\frac{\partial^{i+j}f}{\partial_x^i \partial_y^j}\Big|_{(x,y)=(0,0)}$ and $g_{ij}=\frac{1}{i!j!}\frac{\partial^{i+j}g}{\partial_x^i \partial_y^j}\Big|_{(x,y)=(0,0)}$. + Then + $$L_1 = 3f_{30}+f_{12}+3g_{03}+g_{21}+\reci{\omega}[f_{11}(f_{20}+f_{02})-g_{11}(g_{20}+g_{02})+2f_{02}g_{02}-2f_{20}g_{20}]$$ + (Bautin 1949). +\end{lem} + +Other names for the focal value +\begin{itemize} + \item Lyapunov value + + \item Lyapunov coefficient + + \item Lyapunov constant + + \item Lyapunov quantity + + \item Poincar\'e--Lyapunov coefficient + + \item Poincar\'e constant + + \item Bautin constant + + \item Fokusgröße + + \item Strudelgröße +\end{itemize} + +\begin{exam}[Brusselator] + Given + $$0 \stackrel{\stackrel{\kappa_1}{\rightarrow}}{\stackrel{\leftarrow}{\kappa_2}} X \stackrel{\kappa_3}{\rightarrow} Y$$ + $$2X+Y\rightarrow^{\kappa_4}3X$$ + where $\kappa_1,\kappa_2,\kappa_2,\kappa_2 > 0$ are parameters. We get + $$\begin{aligned} + \dot x&= \kappa_1-(\kappa_2+\kappa_3)x+\kappa_4x^2y\\ + \dot y &= \kappa_3x-\kappa_4x^2y + \end{aligned}$$ + where $x,y\geq 0$. Then the + positive equilibrium is $(x^*,y^*) = \left(\frac{\kappa_1}{\kappa_2},\frac{\kappa_2\kappa_3}{\kappa_1\kappa_4}\right)$. The Jacobian at this point is + $$J=\mattwo{-\kappa_2+\kappa_3}{\frac{\kappa_1^2\kappa_4}{\kappa_2^2}}{-\kappa_3}{-\frac{\kappa_1^2\kappa_4}{\kappa_2^2}}$$ and also + $$\tr J=-\kappa_2+\kappa_3-\frac{\kappa_1^2\kappa_4}{\kappa_2^2}$$ + $$\det J=\frac{\kappa_1^2\kappa_4}{\kappa_2} > 0.$$ + Fix $\kappa_1,\kappa_2,\kappa_4$ and keep only $\kappa_3$ as a parameter + $$\mu(\kappa_3) = \Re \lambda_{12}(\kappa_3) = \half1\left(\kappa_3-\left(\kappa_2+\frac{\kappa_1^2\kappa_4}{\kappa_2^2}\right)\right)$$ + $$\mu'(\kappa_3) = \half1$$ + so the transversality holds. + \begin{enumerate} + \item Shift the equilibrium to the origin + $$\tilde x(t) = x(t)-x^*$$ + $$\tilde y(t) = y(t)-y^*$$ + $$\begin{aligned} + &\dot{\tilde x} = \dot x = \kappa_1-(\kappa_2+\kappa_3)(\tilde x+x^*)+\kappa_4(\tilde x+x^*)^2(\tilde y+y^*)\\ + &\dot{\tilde y} = \dot y = \kappa_3(\tilde x+x^*)-\kappa_4(\tilde x+x^*)^2(\tilde y+y^*). + \end{aligned}$$ + + \item Eliminate $\kappa_3$ by $\tr J = 0$. + $$J = \mattwo abc{-a}.$$ + We define + $$T=\mattwo10{-\frac a\omega}{-\frac b\omega}$$ + so + $$T^{-1} = \mattwo10{-\frac ab}{-\frac\omega b}.$$ + Therefore + $$TJT^{-1} = \mattwo0{-\omega}\omega0.$$ + In general $\dot x = f(x), f(0)=0$. We define $u = Tx$ where $T \in \R^{n\times n}$ is invertible. So + $$\dot u = T\dot x = Tf(x) = Tf(T^{-1}u).$$ + In this case the Jacobian at $u = 0$ is $Tf'(0)T^{-1}$.\\ + Back to the Brusselator: + $$\vectwo uv = T\vectwo{\tilde{x}}{\tilde{y}}$$ + $$\dot u = -\omega v+\left(\frac{\kappa_2^2}{\kappa_1}-\frac{\kappa_1\kappa_4}{\kappa_2}\right)u^2-2\sqrt{\kappa_2\kappa_4}uv-\kappa_4u^3-\frac{\kappa_2^2}{\kappa_1^2}\omega u^2v$$ + $$\dot v = \omega u.$$ + So we get + $$L_1 = -3\kappa_4+\reci\omega(-2\sqrt{\kappa_2\kappa_4})\left(\frac{\kappa_2^2}{\kappa_1}-\frac{\kappa_1\kappa_4}{\kappa_2}\right)=-\frac{1}{\kappa_1^2}(2\kappa_2^3+\kappa_1^2\kappa_4),$$ where we used + $\omega = \sqrt{\det J}=\kappa_1\sqrt{\frac{\kappa_4}{\kappa_2}}$. Hence, $L_1<0$, and the Andronov--Hopf bifurcation is supercritical. Therefore for $\kappa_3$ slightly larger than $\kappa_2+\frac{\kappa_1^2\kappa_4}{\kappa_2^2}$, the repelling positive equilibrium is surrounded by a stable limit cycle. + \end{enumerate} +\end{exam} +In general, we have +$$\dot x(t) = f_\alpha(x(t))$$ +where $x(t) \in \R^n, \alpha \in (-\epsilon, \epsilon), f_\alpha(0)=0$ and +$$\sigma(f_\alpha'(0))=\{\mu(\alpha)\pm \omega(\alpha)i, \lambda_3(\alpha),\dots, \lambda_n(\alpha)\},$$ +where $\mu(0)=0, \omega(0)>0, \mu'(0)\neq 0, \Re \lambda_j(0)\neq 0 \, \forall j \in \jbr{3,n}$. At $\alpha = 0$ there is a 2-dim center manifold. Figure out the behavior there. A similar theorem holds as in 2d, and a recipe for computing the first focal value is available (but not easy). + +\paragraph{Back to 2d:} +What if $L_1 = 0$? Then further work is needed to answer the stability of the equilibrium at the critical parameter value. One has to compute $L_2$ and the formula is roughly one page long and uses up to fifth order derivatives. + +\begin{exam} + Given + $$\begin{aligned} + \dot r &=r(\alpha_1+\alpha_2r^2-r^4)\\ + \dot \theta &= 1. + \end{aligned}$$ + \begin{itemize} + \item If $\alpha_1 < 0$ and $\alpha_2 > 2\sqrt{-\alpha_1}$ then there are 2 limit cycles (the outer one is stable, the inner one is unstable). + + \item If $\alpha_1<0$ and $\alpha_2 = 2\sqrt{-\alpha_1}$, then there is a semistable limit cycle (it attracts solutions from the outside, but repels in the inside). + + \item If $L_2\neq 0$ then we talk about a Bautin bifurcation, where, among other things, the above-described fold bifurcation of limit cycles occurs (with a semistable limit cycle at the critical value). + \end{itemize} +\end{exam} + +\section{Part 2} + +\subsection{Ideas from the General theory of dynamical systems} + +Dynamical systems theory is understanding the long-term behavior of a dynamical system. We will focus on (autonomous) deterministic system. For the whole chapter $X$ is the statespace of a system and all $x\in X$ are the possible states of the system. + +\subsubsection{Continuous vs. discrete time DS} + +In the continuous case a flow is defined like the following: + +\begin{defin} + \item A flow $\phi =(\phi_t)_{t\in\R}$ in $X$ is a family of maps $\phi_t:X\to X$ with $t\in \R$, satisfying $\phi_{s+t}=\phi_s\circ\phi_t$. This is a group of transformations. The elements are invertible, because $\phi_t\circ\phi_{-t}=id_X$. We say, $\phi_t(x)$ is the state at time $t$ where $x$ is the start state. +\end{defin} + +For simplicity, we use the notation $(\phi_t)_t$ for $(\phi_t)_{t\in \R}$. + +\begin{defin} + A semiflow on $X$ is a family $\phi=(\phi_t)_{t\geq0}$ of maps which satisfies $\phi_{s+t}=\phi_s\circ\phi_t$ for $s,t\geq 0$ and $\phi_0 = id_X$. The maps need not be invertible. +\end{defin} + +We can define the same for discrete time systems. + +\begin{defin} + A flow is a family $(T_n)_{n\in\N}$ of maps $T_n:X\to X$ such that $T_{n+m}=T_n\circ T_m$ for all $m,n\in \N$. Then $T_n = \underbrace{T\circ\dots\circ T}_{n-\text{times}} =T^n$, where $T := T_1$. $T^0 = id_X$. +\end{defin} + +For simplicity, we use the notation $(\phi_n)_n$ for $(\phi_n)_{n\in \N}$. + +\begin{exam} + Maps on the interval/circle: + \begin{enumerate} + \item Circle rotation: Fix $\alpha\in\T$. Start at $e^{2\pi ix}$, where $x \in \T$. Rotate by $\alpha$ to get $e^{2\pi i (x+\alpha)}$. + $$T:\T\to\T,\quad Tx = x+\alpha$$ + + \item Angular doubling map: + $$T:\T\to\T, \quad Tx = 2x$$ + + \item Full logistic map: + $$T:[0,1]\to[0,1], \quad Tx = 4x(1-x)$$ + + \item Tent map: Linear interpolation of the points $(0,0),(0.5,1),(1,0)$. + + \item Maps of the square/torus: + \end{enumerate} +\end{exam} + +\subsubsection{Continuous time systems can also give you discrete systems: $(\phi_t)_{t\geq0}$ semiflows of $X$} + +There are different possibilities to convert a continuous semiflow to a discrete flow. We show two of them. + +\begin{enumerate} + \item Fix a constant $\tau>0$ and consider the system at times $0,\tau, 2\tau, \dots$. + $$x, \phi_\tau(x)=:Tx, \phi_{2\tau}(x)=:T^2x,\dots$$ + + \item Poincare section: Let $Y\subseteq X$ be a submanifold of lower dimension such that $\forall y \in Y$ there is a $\tau(y)>0$ (minimal) such that $\phi_{\tau(y)}\in Y$. Then we define the Poincare map of $Y$ as + $$T:Y\to Y, \quad Ty:=\phi_{\tau(y)}\in Y.$$ +\end{enumerate} + +Discrete time systems are Poincare maps $T: Y\to Y$. Let $\tau:Y\to[\epsilon,\infty)$. Define a semiflow on: +$$X=\{(y,s):y\in Y,s < \tau(y)\}$$ +$$\phi_t(y,s):=\begin{cases} + (y,s+t) & s+t < \tau(y)\\ + (Ty,t-(\tau(y)-s)) & \tau(y) \leq t+s < \tau(Ty)\\ + (T^2y,t-(\tau(Ty)-s)) & \tau(Ty) \leq t+s < \tau(T^2y)\\ + \vdots +\end{cases}$$ +In this case, the semiflow starts at $(y,s)$. Then it moves upwards right before it reaches $(y,\tau(y))$. Then it jumps to $(Ty,0)$ and moved upwards. Right before it reaches $(Ty, \tau(Ty))$, it jumps to $(T^2y,0)$ and so on. + +\subsubsection{Relations between systems} + +\begin{defin} + Two maps $T:X\to X$ and $S:Y\to Y$ are conjugate, if there is a bijective $\eta:X\to Y$, such that + $$\eta \circ T=S\circ \eta.$$ + This means that $\eta$ is just a change of coordinates and $S$ represents $T$ in these new coordinates.\\ + \\ + If $\eta$ is just onto, then $\eta$ is a semi-conjugacy (factor map). +\end{defin} + +%\begin{exam} +% $T(a,b) := (Sa,H(a,b))$ +% $$\eta(a,b) := a$$ +%\end{exam} + + +\begin{exam} + Let $X := \R^2, Y := \R$. Now we define maps + $$\begin{array}{ll} + T:X \to X & T(a,b) := (2a,3b)\\ + S:Y \to Y & S(a) := 2a\\ + \eta:X\to Y & \eta(a,b) := a. + \end{array}$$ + Here we can see that + $$\eta(T(a,b)) = \eta(2a,3b) = 2a$$ + while + $$S(\eta(a,b)) = S(a) = 2a$$ + so we conclude that + $$\eta \circ T = S \circ \eta.$$ + Since $\eta$ is surjective, we know that it is a semi-conjugacy, but due to the lack of injectivity, it is not a conjugacy. +\end{exam} + +\subsubsection{Example: Mathematical Billiards "table" $Q \subseteq \R^2$, open} + +Let $Q$ be bounded by $C^3$ curves. We assume that there is no friction and the reflections are elastic. The state of a moving billiard sphere can be represented by an element of $Q\times S^1$ (position and direction). To make sure that the flow is continuous with respect to the time even during a reflection, we have to identify the incoming and outgoing directions on the boundary. It can have very complicated dynamics. + +\paragraph{Poincare sections:} +Let $Y = \partial Q\times S^1$ be the set of the states at the boundaries. Then we can define the collision map $T:Y\to Y$. So if the system starts at $x \in Y$ then $Tx$ is the first point where it hits the boundary. + +\begin{rem} + Such a system is usually not continuous with respect to the starting condition, because a small change of the starting position might change the fact that the flow hits a certain obstacle. +\end{rem} + +\subsubsection{Questions and structure} + +\begin{defin} + For a given $x\in X$ we define the following: + \begin{itemize} + \item Discrete case: Let $T:X\to X$ be a map. Then we define $(T^nx)_n$ to be the forward orbit. + + \item Continuous case: Let $(\phi_t)_{t\geq 0}$ be a semiflow. Then we define $(\phi_tx)_{t\geq0}$ to be the forward orbit. + \end{itemize} +\end{defin} + +\begin{defin} + For $A\subseteq X$ and $T:X\to X$ we use the notation $T^{-n}(A) := (T^n)^{-1}(A)$ for the preimage. +\end{defin} + +Using these definitions, we can ask some questions for $A\subseteq X$: + +\begin{itemize} + \item For given $x\in X$ and $n\in\N$ is $T^nx \in A$ or equivalently, $x \in T^{-n}A$? + + \item Is there a $k\in\N$ such that $T^kx\in A$ or equivalently, $x \in \bigcup_{k\geq 1}T^{-k}A$? + + \item For $x \in A$ are there infinitely many $k\geq1$ such that $T^kx\in A$? (Recurrence) +\end{itemize} + +\paragraph{Coarse structure:} + +Sometime subsets have useful properties. + +\begin{defin} + A set $A\subseteq X$ is called forward invariant, if $TA\subseteq A$. +\end{defin} + +In such a case, we can just study $T|_A:A\to A$. + +\begin{defin} + A set $A\subseteq X$ is called completely invariant, if $TA\subseteq A$ and $TA^c\subseteq A^c$. +\end{defin} + +\paragraph{Topological dynamics:} +Let $X$ be a (often compact) topological space. We can ask some questions. + +\begin{itemize} + \item Does $T^nx$ converge to $y$? Does $y\in \omega(x):=\{\text{Limit points of } (T^nx)_n\}$? + + \item Does $d_X(T^nx,T^ny)$ approach $0$? + + \item Is $x\in\omega(x)$? ($x$ recurrent point) +\end{itemize} +Usually $A$ should be open or closed. We want forward invariant sets to be closed. +In case of a conjugacy, we prefer a topological conjugacy which is additionally a homeomorphism. In the case of differentiable dynamics the set $X$ is a $C^r$-manifold. In the case of measurable dynamics $X$ is a measure space (Ergodic Theory). + +\subsection{Circle rotations} + +Let $X = \T$. We define $A\subseteq \T$ to be an arc (connected subset). We use $\lambda$ as the length of the arc. Let $\alpha \in [0,1]$, and +$$T:\T\to \T, \quad Tx:=x+\alpha.$$ +Obviously, $T$ is invertible and isometric. + +\subsubsection{Rational rotation} + +We assume that $\alpha = \frac pq \in \Q$. Then +$$T^q x=x+q\frac pq=x.$$ + +\begin{prop} + Every orbit is $q$-periodic. So it is recurrent. +\end{prop} + +\begin{rem} + We can predict that if $y$ is in a neighborhood of $x$ then $T^ny$ is close to $T^nx$. +\end{rem} + +\subsubsection{Irrational Rotations} + +We assume that $\alpha \notin \Q$. In this case, every orbit $(T^nx)_{n\geq 0}$ is an infinite set. + +\begin{prop} + Every orbit is dense. +\end{prop} + +\begin{proof} + We show that for all $\epsilon > 0$ the orbit $(T^nx)_n$ is $\epsilon$-dense, meaning that for every $a \in X$ there is a $n\in N$ such that $d(a,T^nx) < \epsilon$.\\ + \\ + Take $\epsilon > 0$ then by Bolzano Weierstraß there exist $m,n$, such that $0<d(T^mx,T^{m+n}x) < \epsilon$. Let $y := T^mx$ and $S:=T^n$. Then $d(y, Sy) < \epsilon$ and $(S^jy, S^{j+1}y) < \epsilon$ for every $j$. So $(S^jy)_j$ is $\epsilon$-dense. Since $(S^jy)_j\subseteq (T^nx)_n$, we know that $(T^nx)_n$ is also $\epsilon$-dense. +\end{proof} + +\begin{cor} + Every $x$ is recurrent. +\end{cor} + +\begin{rem} + We predict that there is no small open set containing the orbit of $y$. +\end{rem} + +\subsubsection{Linear flows on the $2$-torus $\T^2$} +Given +$$\begin{aligned} + \dot x&=\omega_1\\ + \dot y&=\omega_2, +\end{aligned}$$ +where $\omega_1,\omega_2 > 0$. Then +$$(\phi_t(x,y))=(x+t\omega_1,y+t\omega_2).$$ +Let $Y:= \{0\}\times \T$. This is a global Poincare section, because every flow line meets $Y$ infinitely often. Let $T:Y\to Y$ be the Poincare map. So $T(0,y) = (0,y+\alpha)$, where $\alpha=\frac{\omega_2}{\omega_1}$. So $T$ corresponds to the circle rotation by $\alpha$. + +\begin{prop} + The following statements hold. + \begin{enumerate} + \item If $\frac{\omega_2}{\omega_1} \in \Q$ then every $\phi$-orbit is periodic. + + \item If $\frac{\omega_2}{\omega_1} \notin \Q$ then every $\phi$-orbit is dense in the torus. + \end{enumerate} +\end{prop} + +\begin{cor} + Every $\phi$-orbit is recurring. +\end{cor} + +\subsubsection{Some notions of topological dynamics} + +\begin{defin} + A map $T$ on a topological space $X$ is called topologically transitive if it has a dense orbit, meaning that there is an $x\in X$ such that $(T^nx)_n$ is dense. +\end{defin} +This means that under certain conditions, we can go from any open set to any other open set. So all orbits are dense. In this case there is no closed forward invariant set other than $\emptyset$ and $X$ + +\begin{defin} + IThere is no closed forward invariant set other than $\emptyset$ and $X$ then the system $T$ is called minimal. +\end{defin} + +\subsubsection{Distribution of orbits} + +Let $X = \T$, $\alpha \in \R\setminus\Q$ and $Tx=x+\alpha$. Let $A\subseteq \T$ be an arc, consisting of more than one point. Then each orbit intersects $A$. The question is, how many times does the state land in $A$? Let $S_n:\T\to \R$ with +$$S_n(A):=\sum_{k=0}^{n-1}1_A\circ T^k.$$ +Then +$$S_n(A)(x)=1_A(x)+1_A(Tx)+\dots+1_A(T^{n-1}x)$$ +is the number of visits (occupation time) of $(T^kx)_{k=0}^{n-1}$. The relative frequency of visits can be calculated, using +$$\reci nS_n(A).$$ + +\begin{prop}[Equidistribution of orbits] + For all arcs $A\subseteq \T$, we get + $$\limn\frac{S_n(A)(x)}n = \lambda(A),$$ + where $\lambda(A)$ is the Lebesgue measure of $A$. This even converges uniformly in $x\in X$. +\end{prop} + +\begin{defin} + We call the limit the asymptotic frequency of visits to $A$. +\end{defin} + +\begin{lem} + If $A,B\subseteq X$ are arcs with $\lambda(B) < \lambda(A)$, then there is an $N_0\in\Ns$ such that + $$S_{n+N}(A) > S_n(B)$$ + for each $N\geq N_0$ and $n\in\N$. + \label{Monotonicity} +\end{lem} + +\begin{proof} + Since $\lambda(B)<\lambda(A)$ and all orbits are dense, there is $N_0 \in\Ns$ such that $T^{N_0}B\subseteq A$, hence $T^nx\in B$ implies $T^{n+N_0}x\in A$. Therefore + $$S_n(B)\leq S_{n+N_0}(A) \leq S_{n+N}(A)$$ + for all $N \geq N_0$. +\end{proof} + +Let +$$\overline S(A) := \limsup_{n \to \infty} \reci nS_n(A)$$ +and +$$\underline S(A) := \liminf_{n \to \infty} \reci nS_n(A).$$ + +\begin{lem} + The following statements hold: + \begin{enumerate} + \item If $A,B$ are arcs with $\lambda(B) < \lambda(A)$, then + $$\overline S(A) \geq \overline S(B)$$ + on $\T$. + + \item If $A_1,\dots,A_m$ are pairwise disjoint arcs, then + $$\overline S\left(\bigcup_{j=1}^mA_j\right) \leq \sum_{j=1}^m \overline S(A_j).$$ + + \item $\overline S(A) = 1-\underline S(A^c)$. + \end{enumerate} +\end{lem} + +\begin{proof} + We only provide proof for the first two statements. + \begin{enumerate} + \item We use lemma \ref{Monotonicity}. + $$\overline S(B)=\limsup_{n\to \infty} \reci nS_n(B) \leq \limsup_{n\to\infty}\reci n S_{n+N_0}(A) = \limsup_{n\to\infty}\underbrace{\frac{n+N_0}n}_{\to1}\reci{n+N_0} S_{n+N_0}(A) = \overline S(A)$$ + + \item Obviously we get + $$S_n\left(\bigcup_{j=1}^mA_j\right) = \sum_{j=1}^mS_n(A_j)$$ + for a disjoint union. So + $$\limsup_{n\to\infty}\reci n\underbrace{S_n\left(\bigcup_{j=1}^mA_j\right)}_{=\sum_{j=1}^mS_n(A_j)} = \limsup_{n\to\infty}\sum_{j=1}^m\reci nS_n(A_j)\leq \sum_{j=1}^m\limsup_{n\to\infty}\reci nS_n(A_j) = \sum_{j=1}^m \overline S(A_j).$$ + + \item Exercise + \end{enumerate} +\end{proof} + +\begin{lem} + If $A$ is an arc with $\lambda(A) = \reci k$, then $\overline S(A) \leq \reci {k-1}$. +\end{lem} + +\begin{proof} + Take $k-1$ pairwise disjoint arcs $A_1,\dots,A_{k-1}$ of length $\reci{k-1}$ such that $X = A_1 \cup \dots \cup A_{k-1}$. By Lemma \ref{Monotonicity}, there is $N_j \in \Ns$ such that $S_{n+N}(A_j)\geq S_n(A)$ for all $N \geq N_j$. + $$\sum_{j=1}^{k-1}S_{n+N}(A_j)\geq(k-1)S_n(A)$$ + for all $N \geq \max_{j\in \jbr{k-1}} N_j =: \overline N$. The left side is + $$S_{n+N}\left(\bigcup_{j=1}^{k-1}A_j\right)=S_{n+N}(\T)=n+N,$$ + so we get + $$\reci{k-1}\geq \frac{n}{n+N}\reci nS_n(A).$$ + Letting $n$ approach infinity, we get + $$\reci{k-1}\geq \overline S(A).$$ +\end{proof} + +\begin{proof}[Proof of proposition] + Take any arc $A\subseteq X$, $\epsilon > 0$. Choose another arc $B\supseteq A$ such that + $$\lambda(A)\leq\lambda(B)=\frac lk<\lambda(A)+\epsilon$$ + with $k = k(\epsilon)>\reci\epsilon$. Then + $$\overline S(A)\leq\overline S(B)=\overline S\left(\bigcup_{j=1}^lB_j\right)\leq \sum_{j=1}^l\overline S(B_j) \leq \frac l{k-1}=\frac lk\frac{k}{k-1} < (\lambda(A)+\epsilon)\frac k{k-1}$$ + with $B=\bigcup_{j=1}^l B_j$, a disjoint union with $\lambda(B_j)=\reci k$ for $j \in\jbr{l}$. Letting $\epsilon$ approach $0$ and $k$ approach $\infty$, we get + $$\overline S(A)\leq \lambda(A)$$ + Also, $\underline S(A)\geq \lambda(A)$, because of $\overline S(A)=1-\underline S(A^c)$. We conclude that + $$\underline S(A) = \overline S(A) = \lambda(A).$$ +\end{proof} + +\paragraph{An application:} +Take $k\in\Ns$ which is not a power of $10$. Let $p\in\jbr{9}$. Consider $k^j$ where $j\in\Ns$. Let +$$\sigma_n:=\#\{j\in\jbr{0,n-1}: \text{ the decimal expansion of } k^j \text{ starts with } p\}.$$ +Then +$$\limn\frac{\sigma_n}n =\log_{10}(p+1)-\log_{10}(p).$$ + +\begin{exam} + Let $k=2, n=10$ and $p = 1$. Then we take a look at the powers of $2$ up to $2^9$. + $$1,2,4,8,16,32,64,128,256,512$$ + The numbers $1,16$ and $128$ start with $1$, so + $$\sigma_{10}=3.$$ +\end{exam} + +\begin{proof} + The number $k^j$ starts with the digit $p$. This means there exists $l\in\N$ such that $k^j=p\cdot10^l+q$, where $0\leq q < 10^l$. We can write it like this: + $$p = \frac{k^j}{10^l}$$ + Doing some algebra, we get + $$0<\log_{10}(p)=\log_{10}(k^j)-\log_{10}(10^l)= j\cdot\log_{10}k-l<\log_{10}(p+1)\leq1.$$ + Obviously we can choose $l$ such that $j\cdot\log_{10}k-l$ lands in the interval $(0,1]$. Let $\alpha:=\log_{10}k\notin\Q$ and $T:\T\to\T$ with $Tx:=x+\alpha$. Then $T^jx=x+j\alpha$. By the proposition, we get + $$\frac{\sigma_n}{n}=\frac{S_n(A_p)(0)}{n}\to \lambda(A_p).$$ +\end{proof} + +\subsubsection{More general circle maps} + +Let $X = \T$, $\pi:\R\to \T$, $\pi(x) = x \pmod 1$. Let $T:\T\to\T$ be continuous (often a homeomorphism). Recall that rotations are defined such that $Tx = x+\alpha$. If $\alpha \in \Q$ then all orbits are periodic with the same periodicity. Otherwise all orbits are dense. +\newline +\newline +Question: Can we classify rotations?\\ +Recall $S$ and $T$ are topologically conjugate ($T\cong S$) if there is a homeomorphism $\eta:\T\to\T$ such that $\eta\circ T=S\circ \eta$. Equivalently $S = \eta \circ T\circ \eta^{-1}$. + +\begin{defin} + If $T$ has a periodic point, we define $\Per(T)$ to be the smallest $k\in\N$ such that there is a $x\in \T$ which is $k$-periodic. +\end{defin} + +\begin{hw} + Show that if $S\cong T$ then $\Per(S)=\Per(T)$. This means that $\Per(T)$ is invariant under topologically conjugacy. Therfore if $\Per(S) \neq \Per(T)$, we can conclude that $S$ and $T$ are not topologically conjugate. +\end{hw} + +The question is: What happens if $T$ and $S$ are non-periodic? +\newline +\newline +General $T$ can display more complicated dynamics. For example let +$$\Delta_L(x):= Lx-x$$ +be a displacement function where $L:\R\to\R$ satisfies $\pi\circ L = T \circ \pi$. In the case of the rotation, the displacement function is just $\alpha$ which is then $1$-periodic. + +\begin{prop} + If $T:\T\to\T$ is continuous, then there exists a continuous $L:\R\to\R$ with + $$\pi\circ L=T\circ \pi.$$ +\end{prop} + +\begin{defin} + Any such $L$ is a lift of $T$ to $\R$. +\end{defin} + +\begin{proof} + The idea is to keep track of how many rounds the point has done. This number is then added to the position. +\end{proof} + +\begin{prop} + If $T: \T\to\T$, then: + \begin{enumerate} + \item If $L$ is a lift of $T$ then $\{L+m:m\in\Z\}$ is the collections of all lifts. + + \item $L(x+1)-L(x)$ is an integer independent of $x$ and $L$. + \end{enumerate} +\end{prop} + +\begin{defin} + For a given map $T$ we define + $$\deg(T):=L(x+1)-L(x)$$ + to be the degree of $T$. This does not depend on $x$. +\end{defin} + +\begin{rem} + $\deg(T)$ counts how often $T$ maps around $\T$. +\end{rem} + +\begin{rem} + $L(x+m)=L(x)+m\deg(T)$ +\end{rem} + +\begin{prop} + Additionally: + \begin{enumerate} + \setcounter{enumi}{2} + \item If $T$ is a homeomorphism of $\T$, then $L$ is a homeomorphism of $\R$ and $\deg(T)=\pm1$. + \end{enumerate} +\end{prop} + +\begin{rem} + The sign of the degree gives information about the orientation.\\ + $\deg(T)=1$ means $T$ is orientation preserving (o.p.).\\ + $\deg(T)=-1$ means $T$ is orientations reversing (o.r.). +\end{rem} + +\begin{prop} + In addition: + \begin{enumerate} + \setcounter{enumi}{3} + \item $L_\Delta(x) := L(x)-\deg(T)x$ is continuous, bounded, $1$-periodic on $\R$. + + \item $L^m$ is a lift of $T^m$ for all $m\in\Z$. + + \item If $S,T$ are orientation preserving homeomorphisms of $X$ with $S=\eta\circ T\circ \eta^{-1}$ and $L,H$ lifts of $T,\eta$, then $H\circ L\circ H^{-1}$ is a lift of $S$. + \end{enumerate} +\end{prop} + +\begin{proof} + Again, we only prove the first two statements, since the rest is easy to show. + \begin{enumerate} + \item If $L$ is a lift of $T$ then $\tilde L:=L+m$ ist also a lift. If $L,\tilde L$ are lifts then + $$\pi\circ \tilde L = T\circ \pi=\pi\circ L.$$ Therefore $\tilde L(x)-L(x)\in\Z$ for all $x$. Since $\tilde L-L$ is continuous, $\tilde L-L$ is constant. + + \item We easily see that + $$\pi(L(x+1))=T(\underbrace{\pi(x+1)}_{=\pi(x)})=\pi(L(x)).$$ Therefore $L(x+1)-L(x)\in\Z$ is constant. + \end{enumerate} +\end{proof} + +\begin{lem} + Let $T$ be an orientation preserving homeomorphism of $\T$ with lift $L$. Then for $\Delta_L(x) := Lx-x$ we get + $$\Delta_L(x)\leq \Delta_L(y)+1$$ + for all $x,y\in\R$. +\end{lem} + +\begin{proof} + Set $k:=\lfloor y-x\rfloor\in\Z$ and $\theta\in[0,1)$ such that $y=x+k+\theta$. Then + $$\Delta_L(y)=L(y)-L(x+k)+L(x+k)-(x+k)+\underbrace{(x+k)-y}_{=-\theta\leq0} \leq \underbrace{L(y)-L(x+k)}_{\leq 1 \text{ since } y\in[x+k,x+k+1]}+\Delta_L(x+k)$$ +\end{proof} + +\begin{rem}[Recall:] + If $T$ is a orientation preserving homeomorphism of $X$ with lift $L$, then + $$\rho(L)(x):=\limn\frac{L^nx-x}n$$ + exists in $\R$, is an integer and doesn't depend on $x$. So we define + $$\rho(L):=\rho(L)(x)$$ + and we get + $$\rho(L+m)=\rho(L)+m$$ + for all $m\in\Z$. +\end{rem} + +\begin{exam} + Let $T:\T\to\T$ with $Tx=x+\alpha$ and $L:\R\to\R$ with $Lx=x+\alpha$. Then + $$\rho(L)=\limn\frac{x+n\alpha-x}n = \alpha.$$ +\end{exam} + +So we can say that $\rho(L)$ describes the average rotation speed. + +\begin{defin} + We say that $\rho(L)$ is the rotation number of $L$. Also $\rho(T):=\pi(\rho(L))$ is the rotation number of $T$. +\end{defin} + +\begin{rem} + $\rho(T^q)=q\rho(T)\pmod1$ +\end{rem} + +\begin{lem} + If $(a_n)_{n\in\Ns}\subseteq\R$ are such that there exist $k\in\N,\kappa\in\R$ with + $$a_{m+n}\leq a_m+a_{n+k}+\kappa\quad (*)$$ + for every $m,n\in\Ns$, then the following limit exists: + $$\limn \frac{a_n}n\in[-\infty,\infty)$$ +\end{lem} + +\begin{proof} + We split this proof into three parts. + \begin{enumerate} + \item We show that we can assume wlog that $k=0$. Using $(*)$ with the switched roles $m \mapsto n, n\mapsto k, k \mapsto k$, we get + $$a_{n+k}\leq a_n+a_{2k}+\kappa $$ + for all $n\in\Ns$. Therefore + $$a_{m+n}\leq a_m+a_{n+k}+\kappa \leq a_m+a_n+a_{2k}+\kappa$$ + for all $n,m\in\Ns$. Setting $k=0$ and replacing $a_0+\kappa$ by $\kappa$, we get the result + $$a_{m+n} \leq a_m+a_n\kappa.$$ + + \item Now we show that + $$\liminf_{n\to\infty}\frac{a_n}n\in\R.$$ + By induction, we get + $$a_n = a_{1+\dots+1} \leq na_1+(n-1)\kappa.$$ + Therefore + $$\left|\frac{a_n}{n}\right| \leq |a_1|+\frac{n-1}{n}|\kappa| \leq |a_1|+|\kappa|.$$ + We showed that $\left(\frac{a_n}{n}\right)_n$ is bounded, so the limes inferior is real. + + \item In the case $k=0$, let + $$a:=\liminf_{n\to\infty}\frac{a_n}n\in\R.$$ + Take $\epsilon > 0$, we show that + $$\limsup_{n\to\infty}\frac{a_n}n\leq a+\epsilon.$$ + Fix $n\in\N$ such that $\frac{a_n}n < a+\frac\epsilon3$ and $\frac\kappa n<\frac\epsilon3$. Any $l\geq n$ can be written as + $$l=jn+r$$ + with $j\in\N$, $r\in\jbr{0,n-1}$, then + $$\frac{a_l}l=\frac{a_{n+\dots+n+r}}l\leq\underbrace{\frac{ja_n}l}_{j \leq \frac ln}+\frac{a_r}l+\frac{j\kappa}l\leq\frac{a_n}n+\underbrace{\frac{\max(a_1,\dots,a_{n-1})}l}_{l \text{ large}}+\frac\kappa n < a+\frac{\epsilon}{3}+\frac{\epsilon}3+\frac\epsilon3<a+\epsilon$$ + if $l \geq l_0$. + \end{enumerate} +\end{proof} + +\begin{proof}[Proof of Remark.] + We want to show that $\rho(L)(x)=\limn\frac{L^nx-x}{n}$ exists and doesn't depend on $x$. + \begin{enumerate} + \item We claim that $\rho(L)(x)$ is independent of $x$. Since $L$ is a homeomorphism of $\R$ and a lift of a orientation preserving homeomorhpism, we know $L(x+1)=L(x)+1$. So + $$|x-y|<1$$ + implies + $$|L^nx-L^ny|<1.$$ + Hence, for $x,y\in(0,1]:$ + $$\left|\frac{L^nx-x}n-\frac{L^ny-y}n\right|\leq\reci n(|L^nx-L^ny|+|x-y|)<\frac2n\to0,$$ + since $\Delta_{L^n}(x)=L^nx-x$ is $1$ periodic on $\R$. Therefore, if the limit exists then it doesn't depend on the input. + + \item Fix $x\in\R$, let $a_n:=L^nx-x$. We want to show that $\limn\frac{a_n}n\in\R$. Then + $$a_{m+n}=L^{m+n}x-x=\underbrace{L^m(L^nx)-L^nx}_{\Delta_{L^m(y)}}+\underbrace{L^nx-x}_{=a_n},$$ + where $y:=L^nx$. By the lemma, this is less than or equal to + $$\Delta_{L^m}(x)+1+a_n=a_m+a_n+1$$ + for all $m,n\in\Ns$. By the subadditivity lemma we have the limit + $$\limn\frac{a_n}n\in[-\infty,\infty)$$ + and it's also larger than $-\infty$. So + $$\frac{a_n}n = \reci n\sum_{k=0}^{n-1}\underbrace{\Delta_L(T^kx)}_{\geq c > -\infty}\geq c > -\infty.$$ + + \item Rest: Do it yourself. + \end{enumerate} +\end{proof} + +\begin{rec} + $T\cong S$ if they are topologically conjugate. That means that there is a homeomorphism $\eta:\T\to\T$ such that $\eta\circ T=S\circ \eta$. +\end{rec} + +\begin{rec} + For periodic rotations, $\Per(T)$ is invariant: If $S\cong T$ then $\Per(S) = \Per(T)$. The converse is not true. +\end{rec} + +\begin{prop} + Let $T,S: \T\to\T$ be orientation preserving homeomorphisms of $\T$, with $S=\eta\circ T\circ\eta^{-1}$, then $\rho(T)=\rho(S)$. So $\rho(T)$ is an invariant for topologically conjugacy. +\end{prop} + +\begin{exam} + For all $\alpha,\beta \in (0,1]\setminus\Q$ with $\alpha \neq \beta$ and $\alpha \neq 1-\beta$ the corresponding rotations $T,S$ are not conjugate. +\end{exam} + +\begin{proof} + Let $L$ and $H$ be lifts of $T$ and $\eta$. Then $H\circ L\circ H^{-1}$ is a lift of $S$. For $x\in\R$ + $$\frac{(H\circ L\circ H^{-1})^nx-x}n=\frac{(H\circ L^n\circ H^{-1})x-x}n=\frac{H(L^n(H^{-1}x))-L^n(H^{-1}x)}n+\frac{L^n(H^{-1}x)-H^{-1}x}n+\frac{H^{-1}x-x}n$$ + $$=\underbrace{\frac{\Delta_H(L^n(H^{-1}x))}n}_{\to0}+\frac{L^ny-y}n+\underbrace{\frac{\Delta_{H^{-1}}(x)}n}_{\to0} \to \rho(L).$$ + So the rotation numbers coincide. +\end{proof} + +\begin{prop} + If $T:\T\to\T$ is an orienation preserving homeomorphism, then $\rho(T) \in\Q$ if and only if $T$ has a periodic point. +\end{prop} + +\begin{proof} + We show both directions. + \begin{enumerate} + \item $\Leftarrow:$ Suppose $T^qx=x$ for some $q\in\Ns$. Take a lift of $T$, then $L^qx=x+p$ for some $p\in\Z$. Then, $L^{mq}x = x+mp$ for all $m \in \N$. Hence + $$\rho(L)=\lim_{m\to\infty} \frac{L^{mq}x-x}{mq}=\lim_{m\to\infty}\reci{mq}\sum_{k=0}^{m-1}\underbrace{(L^{(k+1)q}x-L^{kq}x)}_{=p}=\frac{mp}{mq}=\frac pq \in\Q.$$ + + \item $\Rightarrow:$ Assume that $\rho(L)=\frac pq$ for some lift $L$ of $T$. Then + $$\rho(L^q)=p\rho(L) = p\cdot\frac pq = p = 0 \pmod1$$ + Therefore $\rho(T^q) = 0$. We show that $S:=T^q$ has a fixed point. We know that $\rho(S)=0$. Take a lift $L$ of $S$ with $L(0) \in [0,1)$. We have + $$\Delta_L(x)=Lx-x\notin \Z$$ + for $x \in \R$ (otherwise: $S(\pi(x))=\pi(L(x))=\pi(x+m)=\pi(x)$, so $S = id$, which has fixed points). Since + $$\Delta_L(0)=L(0)-0=L(0)\in(0,1)$$ + and $\Delta_L$ is continuous on $\R$, $0<\Delta_L<1$ on $\R$. By continuity on $[0,1]$ there is a + $$0<\delta\leq \Delta_L(x)\leq (1-\delta)<1 \quad\forall x \in\R.$$ + Then + $$L^n0=L^n0-0 = \sum_{k=0}^{n-1}\underbrace{(L(L^k0)-L^k0)}_{\Delta_L(L^k0)}$$ + for $n\in\Ns$. Then + $$\frac{n\delta}n \leq \underbrace{\frac{L^n(0)-0}n}_{\to\rho(L)}\leq \frac{n(1-\delta)}n = 1-\delta<1.$$ + Therefore $\rho(L) \neq 0 \pmod1$. This is a contradiction. + \end{enumerate} +\end{proof} + +\subsubsection{Circle homeomorphisms with periodic points} + +\begin{prop} + Let $T:\T\to\T$ be an orientation preserving homeomorphism, $\rho(T)=\frac pq$ with $p,q$ relatively prime. Then, for every periodic point $x$ of $T$: + \begin{enumerate} + \item $x$ has minimal period $q$. + + \item The ordering of $(x,Tx,\dots, T^{q-1}x)$ on $\T$ is the same as the ordering of $(x,Sx,\dots,S^{q-1}x)$ where $Sx:=x+\frac pq \pmod1$. + \end{enumerate} +\end{prop} + +\begin{exam} + Let $T$ be an orientation preserving homeomorphism with $\rho(T)=\frac23$. Let $z$ be a $3$-periodic point. Let $S:\T\to\T$ with $Sx=x+\frac23$. We observe the ordering $(z, Sz, S^2z)$ with $z\in \T$. Those are oriented clockwise. For the points $(z,Tz,T^2z)$ also have the same orientation. +\end{exam} + +\begin{exam} + Suppose that $T$ has exactly one $2$-cycle: $\{x_1,x_2\}$, $Tx_1=x_2$ and $Tx_2=x_1$. So both are fixed points of $S:=T^2$. Without loss of generality we assume that $x_1 = 0$. Then for all $y$ there is an $\overline m\in\{1,2\}$ such that + $$d(T^{2n}y,T^{2n}x_{\overline m}) \to 0$$ + since $T$ is continuous: + $$d(T^{2n+1}y,T^{2n+1}x_{\overline m}) \to 0.$$ + So $d(T^ny,T^nx_{\overline m}) \to 0$ as $n\to\infty$. +\end{exam} + +\begin{thm} + Let $T:\T\to\T$ be a orientation preserving homeomorphism with $\rho(T) = \frac pq$ with $\{x_1,\dots,x_M\}$ of $q$-periodic points, where $x_1,\dots,x_M$ are ordered on a circle. Then for all $m\in\jbr{1,M}$ there is $\overline m\in \{m,m+1\}\pmod M$ such that for all $y \in (x_m,x_{m+1})$ we get + $$d(T^ny,T^nx_{\overline m}) \to 0.$$ +\end{thm} + +Let $C:=\{x:T^qx\}$ be closed. In the case of a rational rotation, $C = \T$. Sometimes $C$ consists of finitely many points. Sometimes $C$ is an interval. + +\begin{lem} + Let $J=[a,b]\subseteq\T$ a closed interval, $f:J\to J$ a homeomorphism, increasing with $f(y)\neq y$ for all $y\in(a,b)$ then for all $y \in (a,b)$ + $$\limn f^n(y)=\begin{cases} + a & \text{if } f(x)<x \text{ on } $(a,b)$\\ + b & \text{ otherwise } + \end{cases}$$ +\end{lem} + +\begin{proof} + Case $f(x) < x$: Then $y>f(y)>f^2(y)>\dots$. This sequence is monotone and bounded, so it has a limit $z$. By continuity, we get $f(z) = z$ and $z=a$. The other case works similarly. +\end{proof} + +If we apply this to $T^q$, then for any $y\in\T\setminus C$ there is an $x\in C$ such that +$$d(T^{mq}y,T^{mq}x)\to0.$$ +By continuoity, we get +$$d(T^{mq+r}x,T^{mq+r}y)\to0$$ +for $r\in\jbr{1,q-1}$ and $m\to\infty$. + +\begin{thm} + For $T$ as above with $\rho(T)\in\Q$, there is a nonempty closed $C\subseteq \T$ of $q$-periodic points (same ordering as for rotation $S$). If $I$ is a maximal interval $\T\setminus C$, then there exists a $x\in \partial I\subseteq C$ such that for all $y\in I$ + $$d(T^ny,T^nx)\to0.$$ +\end{thm} + +\begin{rec} + The $\omega$-limit of $x$ is + $$\omega(x):=\{z\in X: (k_n)_n: k_n\to\infty \text{ and } T^{k_n}x\to z\}.$$ +\end{rec} + +\begin{hw} + If $T$ is continuous: + \begin{enumerate} + \item $\omega(x)$ is closed + + \item $T\omega(x) \subseteq \omega(x)$ + \end{enumerate} +\end{hw} + + +\begin{exam} + In the theorem $\omega(x)=\{x,Tx,\dots,T^{q-1}x\}$ and $\omega(y)=\omega(x)$. +\end{exam} + +Now we take a look at orientation preserving homeomorphisms with no periodic points. So $\rho(T) = \alpha\notin\Q$. + +\begin{rec} + For $Sx:=x+\alpha$, every orbit is dense ($\omega(x)=\T$). +\end{rec} + +\begin{lem} + Let $T$ be as above, $m \in \jbr{n-1}$ and $I$ be a closed arc with endpoints $T^nx, T^mx$ for $x\in\T$. Then for any $y\in\T$ the orbit $(T^ky)_{k\in\N}$ meets $I$. +\end{lem} + +\begin{proof} + We need to show that $X\subseteq \bigcup_{k\in\N}T^{-k}I$. Consider $I_k:=T^{-k(n-m)}I$, where $k\in\N$. Then $I_k,I_{k+1}$ have a common endpoint. Suppose $\bigcup I_k \neq \T$, then $J_m := (I_1\cup\dots\cup I_m)_m$ is growing. The right ends of $J_m$ calling it $(z_m)_m$ points is a monotone sequence. But then, $(z_m)_m$ has a finite limit. So define + $$z=\lim_{k\to\infty} T^{-k(n-m)}(T^mx) = \lim_{k\to\infty}T^{-(k-1)(n-m)}(T^mx) = \lim_{k\to\infty}T^{n-m}(T^{-k(n-m)}(T^mx)) = T^{n-m}z$$ + Therefore $z$ is a periodic point. So we have a contradiction. So $\T = \bigcup_{k\in\N}I_k$. +\end{proof} + +\begin{prop} + Let $T$ be as above, then + \begin{enumerate} + \item $\omega(x)=\omega(y)$ for all $x,y\in\T$. + + \item $E:=\omega(x)$ is a perfect set (it has no isolated points). + + \item $E=\T$ or $E$ is nowhere dense (the interior of the closure is empty). + + \item Cantor set: It's perfect and nowhere dense. + \end{enumerate} +\end{prop} + +\begin{proof} + We only proof the first statement. Maybe we'll do the others in the future. + \begin{enumerate} + \item Take $z\in\omega(x)$, then there exists $(l_n)_n$ going to $\infty$ such that $T^{l_n}x\to z$. Consider $J_n:=[T^{l_n}x,T^{l_{n+1}}x]$ (the shorter interval). By the lemma there is a sequence $k_n\to\infty$: $T^{k_n}y\in J_n$ (fill in the details). + + Since $T^{l_n}x\to z$, we get $d(J_n,z)\to0$. So $T^{k_n}y\to z$ which proves that $z\in \omega(y)$. + + \item Not now + + \item Not now + \end{enumerate} +\end{proof} + +\begin{thm} + Let $T:\T\to\T$ be an orientation preserving homeomorphism of a circle with $\alpha := \rho(T)\notin\Q$. Then there exists a monotone topological semiconjugacy $\eta:\T\to\T$ with $\eta\circ T=S\circ \eta$, where $S$ is a rotation. + + \begin{enumerate} + \item If $T$ is topologically transitive (so $E = \T$), then $\eta$ is a homeomorphism, so a topological conjugate. + + \item Otherwise: $\eta$ is not injective ($S$ is just a factor of $T$). + \end{enumerate} +\end{thm} + +\begin{thm} + Depending on the smoothness of $\eta$ there are different possibilities. + \begin{enumerate} + \item For $C^1$ diffeomorphisms both (1) and (2) are possible. + + \item For $C^2$ diffeomorphisms only (1) is possible. + \end{enumerate} +\end{thm} + +\subsection{Maps with complicated orbit structure} + +\subsubsection{Warmup} + +Very simple maps on the interval/circle can have very complicated dynamics.\\ +Limitations for predictions, often due to: + +\begin{defin} + Let $(X,d)$ be a metric space. The map $T:X\to X$ has sensitive dependence (on initial conditions) if there is a $\delta > 0$ (the sensitivity constant) such that for all $x\in X$ and $\epsilon > 0$ there exists $y\in Y$ such that + $$d(x,y)< \epsilon,$$ + but + $$d(T^nx,T^ny) \geq \delta$$ + for some $n\in\Ns$. +\end{defin} + +\begin{exam}[Prototypical] + Let $X = \T$. + \begin{itemize} + \item Angle doubling map: Let $T:\T\to\T$ with $Tx:=2x$. We take a look at the lift $L:\R\to\R$, with $Lx:=2x$. More generally, we can replace $2$ by an integer $m\geq 2$ where $m=\deg(T)$. In this case, we have $m$ cylinder sets (maximal subintervals, such that $T$ is injective on it). That means that $T|_z$ is injective, where $z$ is a branch. $T^n$ has $m^n$ branches. + \end{itemize} +\end{exam} + +\begin{defin} + A uniformly expanding map on $\T$ is a map $T\in C^1(\T,\T)$ with $|T'|\geq \delta > 1$. So there is a lift $L$. +\end{defin} + +It can be shown that $T^n$ has $m^n$ cylinders and $\diam(Z)\leq \rho^{-n}$ for each cylinder $Z$. Check that we can assume that $T0=0$ (by shifting). + +\subsubsection{Basic properties} + +\paragraph{Periodic orbits:} +We know that $T^n$ has $m^n$ branches. Each branch meets the diagonal at exactly one point. Therefore, there are $m^n-1$ fixed points of $T^n$. So the set of the periodic points is dense (since the $\diam(Z)\to0$ for every cylinder $Z$ as $n\to\infty$). + +\paragraph{Question:} +What about non-periodic points? + +\begin{prop} + Every uniformly expanding map $T$ on $\T$ has sensitive dependence. +\end{prop} + +\begin{proof}[Proof for $Tx=2x$] + If $x\neq y$ with $d(x,y) < \reci4$. Then $d(Tx,Ty)=2d(x,y)$. So we can take $\delta = \reci4$. +\end{proof} + +\begin{itemize} + \item There are always countably infinitely many periodic points. + + \item $T$ has sensitive dependence. + + \item What about other types of orbits? Dense orbits? Recurrent orbits? +\end{itemize} + +\begin{rec} + Continuous map $T$ on $\T$ is topologically transitive if and only if for all open $U,V\neq \emptyset$ there is an $n\in\Ns$ such that $U\cap T^{-n}V\neq \emptyset$. +\end{rec} + +\begin{defin} + $T$ on $X$ is topologically mixing, if for all nonempty open $U,V\subseteq X$ there is a $N\in\N$ such that $U\cap T^{-n}V\neq \emptyset$ for all $n\geq N$. +\end{defin} + +\begin{exam} + No rotation is topologically mixing, since: +\end{exam} + +\begin{prop} + If $X$ has at least three different points and $T$ is an isometry. Then $T$ is not topologically mixing. +\end{prop} + +\begin{proof} + Exercise. +\end{proof} + +\begin{exam} + The doubling map is topologically mixing. Without loss of generality $U,V$ are open intervals. So $\diam(U) > 0$. Take $N$ so large that $\diam(U)>2\cdot 2^{-N}=\diam(Z)$ where $Z$ is a cylinder of $T^n$. In this case there is a cylinder $Z_0$ lying completely in $U$. So $\T = T^nZ_0\subseteq T^nU$. +\end{exam} + +\begin{prop} + Every uniformly expanding circle map $T$ is topologically mixing. +\end{prop} + +\begin{proof} + Same argument: $T^N$ has $m^n$ branches/cylinders $Z$ with $TZ = \T$. We know that $\diam(Z)\leq \rho^{-N}$ and do the same. +\end{proof} + +\begin{prop} + $T$ as above has dense orbits. +\end{prop} + +\begin{prop} + If $T\in C(X,X)$ and $X$ has at least $2$ points, then topologically mixing implies sensitive dependence. +\end{prop} + +\begin{proof} + Exercise. +\end{proof} + +\subsubsection{Symbolic dynamics and coding} + +The case of the doubling map $T:\T\to\T$ with $Tx = 2x$. +\newline +\newline +Binary/dyadic expansions: +$$x = 0.\omega_0\omega_1\omega_2\dots = \sum_{j\in\N}\frac{\omega_j}{2^{j+1}},\quad \omega_j\in\{0,1\}.$$ +We can imagine that $\omega_0$ splits the interval into two pieces. If $\omega_0=0$ we use the left piece. Otherwise we use the right one. Then we keep doing it with $\omega_1,\omega_2,\dots,\omega_{l-1}$ to get a smaller interval. We get the interval +$$\left[\sum_{j=0}^{n-1}\frac{\omega_j}{2^{j+1}},\sum_{j=0}^{n-1}\frac{\omega_j}{2^{j+1}}+\reci{2^r}\right] =: Z_{(\omega_0,\omega_1,\dots,\omega_{r-1})}.$$ +Now our map $T$ can simply be written as +$$Tx=\omega_0+\sum_{j\in\N}\frac{\omega_{j+1}}{2^{j+1}} = \sum_{j\in\N}\frac{\omega_{j+1}}{2^{j+1}} = 0.\omega_1\omega_2\dots$$ +Also +$$T^nx=0.\omega_n\omega_{n+1}\dots$$ +So $T^nx\in Z_{(\omega_n,\dots,\omega_{n+r-1})}$ for all $r,n \in \N$. For every $\omega = (\omega_j)_{j\in\N}\in\Omega_2:=\{0,1\}^{\N}$ there exists an $x$ such that $x=0.\omega_0\omega_1\dots$ + +\paragraph{Application:} +\begin{enumerate} + \item $T$ has $2^p-1$ points of period $\leq p$: So there exists $2^p$ tuples $(\omega_0,\dots,\omega_{p-1})$. Take $\omega=\overline{(\omega_0,\dots,\omega_{p-1},\dots)}$ + + \item $T$ has dense orbits: Take $\omega$ which contains every finite block: + $$\omega=0,1,00,01,10,11,000,\dots, \hat \omega_0,\dots,\tilde \omega_{r-1},\dots$$ + $\eta:\Omega_2\to\T$ + $x := \eta(\omega)$, $T^nx=0.\tilde\omega_0,\dots,\tilde\omega_{r-1}\in Z_{(\omega_0,\dots,\omega_{r-1})}$. So the orbit lands in every cylinder and is therefore dense. + + \item There exists $x\in Z_{(0,0,1)}$ such that $T^nx\in Z_{(0,0,1)}$ for all $n\geq 2$. Take $\omega=0,0,1,0,1,0,1,0,1,0,1,\dots$. Such that only one time there are zwo consecutive zeros. In this case, the orbit will never return to the first quater. + + \item For every left-/right sequence there is a 0-/1 sequence. So there is a $x$ such that $T^nX$ on left/right of presented times. + + \item The shift means: $T$ can be represented on $\Omega_2$ by + $$\sigma:\Omega_2\to \Omega_2$$ + the shift map with $\sigma((\omega_j)_j) := (\omega_{j+1})$. So we get a commuting diagram with $\sigma$, $\eta$ and $T$. In this case $\eta$ is a semi conjugacy (but not injective because of different expansions for the same number). +\end{enumerate} + +\paragraph{Metric on $\Omega_2$:} +Let $\omega:=(\omega_j)_j, \tilde \omega:=(\tilde \omega_j)_j$. Let $s(\omega,\tilde\omega):=\inf\{j\in\N:\omega_j\neq\tilde\omega_j\}\in[0,\infty]$. Now let $d(\omega,\tilde\omega):=2^{-s(\omega,\tilde\omega)}$. Now let +$$[\omega_0,\dots,\omega_{r-1}]:=\{\tilde\omega:\tilde\omega_j=\omega_j\quad j \in \jbr{0,r-1}\}.$$ +This is a $2^{-r}$ neighborhood of $\omega$, a cylinder set in $\Omega_2$. + +\begin{prop} + The following statements hold: + \begin{enumerate} + \item $d$ is a metric. + + \item $\eta$ is continuous. + \end{enumerate} +\end{prop} + +However $\eta$ is not injective in this situation: +$$\omega_0\dots\omega_{r-1}10000000\dots = \omega_0\dots\omega_{r-1}01111111\dots$$ +Such $x$ have exactly two preimages. These $x$ are exactly the endpoints of the diadic intervals. All other $x$ have exactly one preimage $\omega$ such that $x=\eta(\omega)$. +\newline +\newline +We imagine that we half the interval and shrink both parts. Then we repeat it and get something similar to the cantor set. + +\begin{prop} + $\Omega_2$ has no isolated points and is totally disconnected and compact. So this is a cantor set. +\end{prop} + +\subsubsection{The general uniformly expanding circle maps $T:\T\to\T$ of degree 2} + +Let $Z_0,Z_1$ be the two cylinders. So the natural semipartition is $S = \{Z_0,Z_1\}$ with overlapping endpoints. Previously $x\in Z_{(0,1,0)}$ meant $x \in Z_0$, $Tx\in Z_1$ and $T^2x\in Z_0$. The same holds for this general case. +$$Z_{(\omega_0,\dots,\omega_{r-1},\omega_r)} := \text{The non degenerate interval in } Z_{(\omega_0,\dots,\omega_{r-1})}\cap T^{-r}Z_{\omega_r}$$ +Then $x\in Z_{(\omega_0,\dots,\omega_{r-1})}$ implies $T^jx\in Z_{\omega_j}$ for $j\in\jbr{0,r-1}$. Moreover for every $\omega=(\omega_j)_j\in\Omega_2$ there exists exactly one $x = \eta_T(\omega)\in\T$ such that $x \in Z_{(\omega_0,\dots,\omega_{r-1})}$ for all $r\in\Ns$. Indeed +$$\bigcap_{r\in\Ns} Z_{(\omega_0,\dots,\omega_{r-1})}$$ +is a singleton because it's a nested sequence of non empty compact intervals and $\diam(Z_{(\dots)}) \leq \rho^{-r} \to 0$. :)\\ +So we define $\eta_T:\Omega_2\to\T$ like that. For $x = \eta_T(\omega)$, consider $y := Tx$. Then $T^jy=T^{j+1}x\in Z_{\omega_{j+1}}$ for all $j\in\N$. So +$$\eta_T\circ \sigma = T\circ \eta_T.$$ +Check the following: +\begin{enumerate} + \item $\eta_T$ is continuous. + + \item $x$ has two preimages if and only if $x$ is the endpoint of some cylinder. This looks like + $$\omega = \omega_0\dots\omega_{r-1}10000000\dots,\tilde \omega= \omega_0\dots\omega_{r-1}01111111\dots.$$ + with $\eta(\omega)$, define $\eta_T^{-1}(x) := \omega$ (not $\tilde \omega$). +\end{enumerate} + +\begin{thm} + Any two uniformly expanding circle maps $T, \tilde T$ of degree $2$ are topologically conjugate. Hence they are isomorphic to the doubling map. +\end{thm} + +\begin{proof} + Let $\psi:= \eta_{\tilde T}\circ\eta_T^{-1}:\T\to\T$. Then + $$\psi\circ T=\tilde T\circ \psi.$$ + Also $\psi$ is a bijection. \\ + Claim: $\psi$ is a homeomorphism. It suffices to show that it's continuous at every $x\in\T$ (by changing the roles of $T, \tilde T$).\\ + Let $\epsilon > 0$. Let $Z_{(\omega_0,\dots,\omega_{r-1})}$ be a cylinder of $T$ and $\tilde Z_{(\omega_0,\dots,\omega_{r-1})}$ be a cylinder of $\tilde T$. Take $r\in\Ns$ so large that choose four adjacent cylinders $\tilde Z(l) = \tilde Z_{(\omega_0^{(l)},\dots,\omega_{r-1}^{(l)})}$ where $l\in\jbr{1,4}$ such that $y$ is between $Z(1)$ and $Z(4)$ and all of them are contained in the $\epsilon$ neighborhood. Consider $Z(l) = Z_{(\omega_0^{(l)},\dots,\omega_{r-1}^{(l)})}$ where $l\in\jbr{1,4}$. By construction $Z(l)$ is mapped to $\tilde Z(l)$. Choose $\delta > 0$ such that $B_\delta(x)\subseteq \bigcup_{l=1}^4Z(l)$. Then + $$\psi(B_j(x))\subseteq \psi\left(\bigcup_{l=1}^4Z(l)\right)=\bigcup_{l=1}^4\tilde Z(l)\subseteq B_\epsilon(y).$$ +\end{proof} + +\begin{rem} + Analogous construction works for degree $m\geq 2$ maps with the sequence space $\Omega_m:=\jbr{0,m-1}^\N=\{(\omega_j)_{j\geq0}:\omega_j\in\jbr{0,m-1}\}$. +\end{rem} + +\begin{thm} + Two uniformly expanding circle maps $T, \tilde T$ of degree $m$ and $\tilde m\geq 2$ respectively are topologically conjugate if and only if $m=\tilde m$. +\end{thm} + +\begin{proof} + We look at the two cases. + \begin{itemize} + \item $m=\tilde m$: The same as seen before. + + \item $m\neq \tilde m$: The number of preimages of a point $(m,\tilde m)$ is invariant under conjugaticy. + \end{itemize} +\end{proof} + +\subsection{Outlook: Coding for other systems} + +\begin{defin} + For arbitrary $X$ and $T:X\to X$ and a partition $S=\{Z_i\}_{i\in I}$, where $I$ is finite/countable. For any $x\in X$ the $S$-itineray ($S$-name) of $x$ is the sequence + $$\gamma_T(x):=\omega=(\omega_j)_{j\in\N}\in\Omega_I=I^\N,$$ + with $T^jx \in Z_{\omega_j}$ for all $j\in\N$. So $\gamma_T:X\to \Omega_I$. +\end{defin} + +For $y = Tx$, we get $T^jy=T^{j+1}x \in Z_{\omega_{j+1}}$ that means that $\gamma \circ T = \sigma \circ \gamma$. + +\paragraph{Warning:} +In general, $\gamma$ is not injective. For example, $S = \{X\}$ doesn't tell anything. We want that +$$Z_{(\omega_0,\dots,\omega_{r-1})}:=\bigcap_{j=0}^{r-1}T^{-j}Z_{\omega_j}$$ +shrinks to at most one point. + +\begin{rem} + Sometimes, it is useful to use partitions with overlaps. +\end{rem} + +\begin{rem} + In general, even for nicest $S$, $\gamma_T$ need not be surjective. And $\gamma_T(X) \subseteq \Omega_I$ can be very complicated. +\end{rem} + +\begin{exam} + Let $T:\T\to\T$ a surjective piecewise not continuous linear map. We assume that the graph doesn't contain $[0.5,0.5]^2$. Then $\gamma_T(X)=\{\omega: (\omega_j,\omega_{j+1})\neq(1,1)\quad \forall j\in\N\}$. +\end{exam} + +It $T$ is invertible, use $2$-sided sequences +$$\hat\Omega_I:=\{\og=(\og_j)_{j\in\Z}:\og_j\in\Z\}=I^\Z$$ +$$\hat\Omega_I\to\hat\Omega_I, \quad (\omega_j)_{j\in\Z}\mapsto (\og_{j+1})_{j\in\Z}$$ +and we define $\gamma_I(x)=(i_n)_{n\in\Z}$, where $T^nx\in Z_{i_n}$ for all $n\in\Z$. + +\begin{exam} + Baker map on $\T^2$. Let $Z_0$ be the closed left half and $Z_1$ be the closed right half. Then $\{Z_0, Z_1\}$ is almost a partition. Let $T:\T^2\to\T^2$ with + $$T(s,t) = \left(2s,\half t+\half{1_{Z_1}(s,t)}\right).$$ + Then for all $\og\in\hat\Og_I=\{0,1\}^\Z$ there exists an $x$ such that $\gamma(x)=\og$. If we restrict ourselves to the first component of $T$, we get + $$S(s) = 2s.$$ + This is an example of a general hyperbolic map with expanding (horizontal) and contracting (vertical) directions. +\end{exam} + +\subsubsection{Outlook: Measurable dynamics (Ergotic theory)} + +We have already seen chaotic maps with sensitive dependence transitivity (coexistence of diffent types of orbits). What do most/many orbits do? + +\begin{exam} + Doubling map $T:\T\to\T$, $Tx = 2x$. Let $f:= 1_{Z_1}$ and $X_k \in f\circ T^k:\T\to\{0,1\}$. Then + $$x \in Z_{[\og_0,\dots,\og_{n-1}]}$$ + if and only if + $$T^kx\in Z_{\og_k}$$ + for all $k \in\jbr{0,n-1}$. Also $\lambda(Z_{[\omega_0,\dots,\og_{n-1}]})=2^{-n}$. Suppose we split $x$ at random, using $P = \lambda$ (the Lebesgue measure on $(X, B_X)$). Then + $$P[(X_0,\dots,X_{n-1})=(\og_0,\dots,\omega_{n-1})]=\lambda(Z_{(\og_0,\dots,\og_{n-1})})=2^{-n}$$ + This deterministic dynamival system generates the most random process possible if the initial condition is regarded random.\\ + Recall that the strong law of large numbers implies + $$\reci n\sum_{k=0}^{n-1}X_k \to \half1$$ + almost sure. This is a special case of the Ergotic theorem (for the doublong map): + $$\forall f \in L^1(\lambda): \reci n\sum_{k=0}^{n-1}f\circ T^k \to \int fd\lambda \text{ almost everywhere}.$$ +\end{exam} + +\begin{thm} + Let $A \in B_X$ be any measurable set and $f:=1_A$. Then + $$\reci n\sum_{k=0}^{n-1}1_A\circ T^k \to\lambda(A) \text{ almost everywhere}$$ +\end{thm} + +What is behind this? +\begin{thm} + Suppose $T$ is measurable on a measurable space $(X,B_X)$ such that for all $A\in B_X$ the exists $\mu(A) \in[0,1]$ such that + $$\reci n\int_{k=0}^{n-1}1_A\circ T^k \to \mu(A)$$ + then + \begin{enumerate} + \item $\mu$ is a measure on $B_X$ and $\mu(X)=1$ (showing the finite additivity is easy, but not the $\sigma$-additivity) + + \item $\mu$ is $T$-invariant: $\mu\circ T^{-1}=\mu$, meaning that $\mu(T^{-1}A)=\mu(A)$ for all $A\in B_X$. + \end{enumerate} +\end{thm} + +\begin{proof} + We only prove the second property. Since $1_{T^{-1}A}=1_a\circ T$, we get + $$\underbrace{\reci n\sum_{k=0}^{n-1}1_{T^{-1}A}\circ T^k}_{\to\mu(T^{-1}A)}=\reci n\sum_{k=1}^{n} 1_A\circ T^k= \underbrace{\reci n\sum_{k=0}^{n-1}1_A\circ T^k}_{\to \mu(A)} \underbrace{-\reci n1_A+\reci n1_A\circ T^k}_{\to0}.$$ + So we conclude that $\mu(T^{-1}A) = \mu(A)$. +\end{proof} + +The existence of $T$-invariant probability measure $\mu$ enables quantitative analysis of $T$, for example, the ergodic theorem implies that +$$\reci n \sum_{k=0}^{n-1}1_A\circ T^k \text{ converges } \lambda-\text{almost everywhere}.$$ +This is in particular useful if $\mu$ is equivalent to $\lambda$ (meaning they have the same $0$-sets) + +\begin{exam} + If $T$ is a uniformly expanding circle map and $C^2$ (or $C^{1+\epsilon}$) then there is a $\mu\circ T^{-1} \cong \lambda$. +\end{exam} + +\begin{exam} + Rotations preserve $\lambda$. +\end{exam} + +\begin{exam} + Any Hamiltonian system has an invariant measure $\cong \lambda^d$ (Liouville measure), which is finite on compact subsetes. +\end{exam} + +\begin{exam} + Math billiards. +\end{exam} + +Sample result: Poincare-Carathedory recurrence theorem. + +\begin{thm} + Let $(X, B_X, \mu)$ be a finite measure space and $T$ be measurable with $\mu = \mu \circ T^{-1}$. Then for all $B \in B_X$ and $\mu$-almost all $x\in B$ will return to $B$ infinitely often. That means that there is an increasing, diverging sequence $(n_k)_k$ such that $T^{n_k}x \in B$. +\end{thm} + +\begin{proof} + Let's go through the proofs. + \begin{enumerate} + \item We say that $A\in B_X$ is a wandering set if no $x\in A$ returns. So $A$ and $T^{-k}A$ are disjoint for all $k\in\Ns$. Applying $T^{-m}$ to both sets, we get that $T^{-m}A$ and $T^{-m-k}A$ and so + $$A, T^{-1}A, T^{-2}A, \dots$$ + are pairwise disjoint. Then we get, + $$\infty > \mu(x) \geq \mu\left(\bigcup_{k\in\N}T^{-k}A\right)=\sum_{k\in\N}\mu(T^{-k}A) = \sum_{k\in\N}\mu(A) = \infty\mu(A).$$ + Therefore $\mu(A) = 0$. + + \item Take any $B\in B_X$. Let + $$A:= B\setminus\bigcup_{k\in\Ns}T^{-k}B,$$ + the set of returning points. Then $A$ is wandering. By 1. we know that $\mu(A)=0$. But + $$\mu(\{x\in B: x \text{ is not infinitely recurrent to } B\}) = \mu\left(\bigcup_{n\in\N}T^{-n}A\right)\leq\sum_{n\in\N}\underbrace{\mu(T^{-n}A)}_{=\mu(A) = 0} = 0.$$ + \end{enumerate} +\end{proof} + +\end{document} diff --git a/dyn_sys/prog/.ipynb_checkpoints/prog_dynsys-checkpoint.ipynb b/dyn_sys/prog/.ipynb_checkpoints/prog_dynsys-checkpoint.ipynb @@ -0,0 +1,56 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "a379166d-b517-48eb-b85c-9b2738f2aa7c", + "metadata": {}, + "outputs": [ + { + "ename": "ModuleNotFoundError", + "evalue": "No module named 'maptplotlib'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[2], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmaptplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n\u001b[1;32m 2\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n", + "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'maptplotlib'" + ] + } + ], + "source": [ + "import maptplotlib.pyplot as plt\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cc2070c2-97c1-43fb-a158-bb9b832f44a3", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "iiadp_env", + "language": "python", + "name": "iiadp_env" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/dyn_sys/prog/prog_dynsys.ipynb b/dyn_sys/prog/prog_dynsys.ipynb @@ -0,0 +1,363 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "a379166d-b517-48eb-b85c-9b2738f2aa7c", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "id": "71fc9a4a-4346-4703-8c01-4565b0c6f0ea", + "metadata": {}, + "source": [ + "# Exercise 1\n", + "scketching phase portrait" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "cc2070c2-97c1-43fb-a158-bb9b832f44a3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "<matplotlib.quiver.Quiver at 0x7f9c03c19d50>" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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URSwWl/io7CFDhpT6RFXHDevnxo4dW2IlHzRoEL569Yp1NKVs2LCh1CesvMMv6ujPP/8sc6fQs2dPPHjwoNo3U4j/nsci75Wop6cn/vLLL2rf6Obm5so9RKHuh1s+Z2NjI3fnpq2tjR07dsQlS5bg5cuX1eozST7n4eGh0I7azc0N586di8eOHVOrw0bFStv2ltd07Ny5U6bpKA01Igo4duwYamlpyTQhiP9O3ar7px1+7vbt2wgAaGxsjAcOHFC7lVxR4eHh0uawW7duanVehDJSU1Olb7XTpMMvXxIKhTLvgGnTpg3+/PPP+OHDB9bRlMJxnMw7XwwNDdHHxwcPHTqkkncMqJKXl5fMjkGdD7fI8+WOr/jDw7777ju8ceOGWr89/XOLFy8usbMu/rCwTZs2YXBwsNqet/a5zZs3V7rpKI0y++//7H/fHTt2LFhbW4OHh4fMf9Nt3Lgxu1AV0L17d9i1axf06dMH7OzsWMepsJYtW8KPP/4I7dq1A29vb7X+N+Hy1K1bF5YtWwYWFhYwceJEtf9PsWXR09ODefPmQUFBAYwfPx6cnJxYR6oQHo8HkydPhsjISBgyZAj06tULjIyMWMeqkK+++grMzMygd+/e0Lt3b434L6+l8fb2hrS0NOjWrRt4enpC+/btwcDAgHUspXXr1g0ePnwInTp1And3d3B3d1f7/yxcmg4dOkDbtm3B1dVVOpycnKr1MeEhKvD/qRnJzs4GPp8PAoFAYzfohBBCyH+NMvtvrWrKRAghhBBSAjUihBBCCGGGGhFCCCGEMEONCCGEEEKYoUaEEEIIIcxQI0IIIYQQZqgRIYQQQggz1IgQQgghhBlqRAghhBDCDDUihBBCCGGGGhFCCCGEMEONCCGEEEKYoUaEEEIIIcxQI0IIIYQQZqgRIYQQQggz1IgQQgghhBlqRAghhBDCDDUihBBCCGGGGhFCCCGEMEONCCGEEEKYoUaEEEIIIcxQI0IIIYQQZqgRIYQQQmqAwsJCiIqKgtzcXNZRlKLDOgAhhBD18P79e4iIiABDQ0MwMjICIyOjEt/r6+sDj8djHbVCUlJSYOLEiaCnpwdmZmbSUadOHZmfiy/j8/mgra3NOrbC9PX1YenSpXD+/HmoVasW1KtXD6ytrWXGl5dZWlqCjg7bVoCHiMg0gRzZ2dnA5/NBIBCAiYmJSu8rNjYWateuDRYWFiq9HxYQEf7880/w9PQEU1NT1nGqFMdx8Pz5c7h9+zZMnjwZ6tatyzpSlRCJRPD+/XuIjIyEyMhIiI+Ph0WLFkGjRo1YR1MYx3GQk5MDAoEAsrKyZMaXlxUWFoKfnx+0bt2adWy5bt26Bdu2bQNELHdwHCf9Xk9PD1auXAkeHh6sS5ArLy8PvLy84OnTp2Uuw+PxZBoUQ0ND4PP58O2338LgwYOrMW3FnDt3DoYNG6bQsjweD0xNTaFu3bqwbNkymDx5sto3YQKBANq3bw+RkZEKLc/j8cDS0hJ8fX1h0aJFoKurWyU5lNp/oxoTCAQIACgQCFR+P05OTlhQUKDS+2Hh3r176O7ujhMmTGAdpcqkpqbi0aNHcfz48Vi3bl0EAPz9999Zx1KaWCzG6OhovH79Om7btg3nzZuHffv2xSZNmqCWlhYCAAIAmpqaYmBgIOu4Cjlz5gw2btwYTU1NkcfjSWuQN5o1a4YvXrxgHV0hHMfhnDlzFKqreLi5uWFoaCjr6ApLTk7Gxo0bK1yfp6cnhoWFsY6tMJFIhGPHjlW4vj59+mjE48dxHMbGxuLZs2dxxIgRCtfXv39/lTz/lNl//+cbEbFYjAMGDEBLS0uV3QcLr169wgEDBiAAoJ6eHsbGxrKOVGFFRUV4//59XLlyJbZv377EDu6HH35gHVFhly5dwkGDBqGDgwPq6emVu5GwsbHRqI08IuKvv/6q8EZw5MiRKn+hUdWEQiF6eHiUW5uenh6uW7cOi4qKWEdWSG5uLv7111+4dOlSbNasWbn1WVlZ4dGjR5HjONbR5UpLS8NLly6hn58fenp6oqGhoULrZsuWLfHq1atqWd/nTceKFSvQ29sbLSwslGqQO3XqhPfu3VNZRrVsRNatW4cAgAsWLFD4NtXRiCxevBgBAF1dXVV2H9UpNjYWJ0yYILOz9vX1ZR1LaR8/fsQDBw7gyJEjsU6dOmU+mSZOnKiWG4qyFBUV4dKlSxXaUDg5OWFCQgLryEqLj4/Hrl27lruT3rFjh8Y8dgKBAE+dOoXjx4+Xuz4Wj/bt26t9AykUCjEwMBBXrVqF3bp1Q11dXYXWSy0tLZw/fz5mZWWxLqEEiUSCYWFhuGfPHpw0aRI2b95cqZ0zAKCFhQUGBASoTQNZFU3H56NVq1Z48eJFlT/31K4Refz4MTZu3BidnZ3VqhHZt2+f9MHx8fFRyX1Ul/T0dPT19S3xKtvExATT09NZx1NYbGwsuru7K/SE6t69OwqFQtaRlcZxHM6YMUNubV5eXmq5oS9LTk4OHjlyBHv27FnuIZmmTZvi8+fPWUcuV1xcHG7fvh379Omj8E5aT08P169frzY7sc+JxWJ8+vQpbtiwAb29vdHIyEjpnZi7u7taPXYCgQBv3LiBP/zwA3p7eyOfz1eoDnt7e7Sysirx2C1ZsgQzMzOZ1VPZpsPCwgK9vb1xxYoV6OzsLHNdo0aN8PDhwygWi6ulFrVqRHJyctDe3h5v3LiBnp6eatOI3L17V2bjMm/evCq/j+qQl5eHP/30E5qYmJS6Yq5du5Z1RKXFxMSgj4+P3Cdcy5YtMSMjg3VUpYhEIvz999/RyclJbm2jRo3CwsJC1nHLJZFI8ObNmzhhwgSsVauWQhvKESNGqO2hGIlEgk+ePMGVK1dimzZt5NbRuHHjEocvOnTogK9fv2ZdhhTHcfj69Wv87bff0MfHB01NTeXWxOPxsF27drhkyRK8du2azKyWubk57tu3DyUSCdN6oqKi8MiRIzhr1ix0dnaWOZeqrGFgYIDdunXD5cuX459//ompqamIiNiiRQvpMsOHD8eoqKhqr6eqmo6zZ89iXFycdJZDIpFIf5eFhQVu2bJF5dsUjuPww4cPePXqVVy/fr30PBW1aEQmTJiACxcuREQstxEpLCxEgUAgHQkJCSppRKKiotDc3FzmQf3555+r9D5UraioCHfv3o316tUrc0WtV68e5ubmso5aIVevXi1zw2lpaYkxMTGsIyosLy8Pt23bho0aNSp347Jo0SKmG3tFREREoJ+fH9ra2pZag7a2Ng4YMEDmhEA9PT0MCAhQu0MxBQUFeOXKFZw5cybWr19f7mPTsWNHXLt2LYaGhiLHcdJzsPT19XHDhg1qMQvy/v173LdvH44dOxatra3LXd9atmyJc+bMwXPnzuGnT5+kv4fjOOkhqOnTpzOZVc3Pz8egoCDcsGEDDhkyBC0tLRXaQdva2uKoUaNw69at+OTJExSJRCV+d1JSEgL8eyJxUFCQymtRZdNRmufPn2Pt2rVx1apVmJ2dXeX15OXl4ePHj3Hfvn04f/589PLyQjMzs1KzM29E/vjjD2zdurX03SjlNSL+/v4VLkRRWVlZ2LJlyxL3ceLEiSq7D1XLyMhALy+vclfe3bt3s46qtJSUFBwzZkyZNRkaGuKjR49Yx1RIeno6/vDDDyWaXoB/D5ktX74cDQwMpJdt3ryZdeQypaen4/bt27FDhw5lPjYuLi7466+/YnJyMiIirl69GgEAmzRpgs+ePWNcwf9JTU3FgwcP4tChQ+UenjA0NMTBgwfjvn37MCkpqcTvady4MXbs2BHDw8MZVPGvpKQkPH78OE6dOhXt7OzK3SY0atQIp0yZgkePHsXExMQyf++7d++wbdu2+PDhw2qr5cOHD3jq1ClcuHAhduzYUaHDYTo6OtihQwdcuHAhnjp1SuFzqoKCgvD3339XSdNf3U1HaV6/fo0pKSmVrkUikeD79+/xwoULuHr1ahw+fDg2b95c4XfEMW9E4uPj0dLSEl++fCm9jPWMSFFREXp7e5f6x7p//36V3Ed1EYvFePfuXRw4cGCp9TRv3lwtXqEpiuM4PHjwYImu+vOfeTwenjt3jnXUcsXFxeGCBQtK3clZW1vjhg0bpOd/6OnpoZ6eHv7xxx+MU5ckFArx3Llz6OPjU+ZOwdraGv/3v//JPM+LTZ8+HYcPH878XBeO4zA8PBzXr1+PnTt3lrsRtbKywmnTpuGff/6JeXl5Zf7OwsJC3LRpU7Udby+WkZGB58+fx3nz5qGjo2O5OwFLS0scPXo07t27F6OjoxXeoWVlZam0NpFIhE+ePMGtW7fi6NGjsWHDhgrt1OrWrYtDhgzBDRs2YGBgIObn56ssoyKqsuk4d+5chZqOqiIQCDA4OBh37NiBs2bNws6dO6OxsbHCtQD8ewivR48euHDhQty+fTv7RuT8+fMI8O80bfEo3ploa2srtJJX9Tki7969wz179mBAQECJP2B8fHyV3Ed1SkpKKnP69cyZM6zjKWX06NElapg6dSqmp6ejjo4OAqj3jEGxgIAAad7Ph729Pe7Zs0fms2o4jkM+n4+3b99mmLh0t2/fLnOq1cDAAMeMGYPXrl2T2+w+evSI+aGY6Ojoct+K2rp1a1yxYgWGhISo7WGx/Px8dHNzK/ecCD6fj0OGDMGtW7diWFgY879/aQYPHqzQW2h5PB46OzvjrFmz8MiRIxgVFaVW9cydO1djm47P/fTTT0p9bgwAoK6uLjo7O+P48eNx48aNeP36dUxMTJSpR5n9t8o+17Vnz54QGhoqc9nkyZPBwcEBli1bxuRjc+3t7cHe3h4iIiLA09MTnjx5Aj4+PnDixAmoV69eteepLCsrKxg5ciRs27YN9PX1QSgUAgBAhw4d4KuvvmKcTjkDBw6EEydOAMC/j9OePXvAy8sLAADq1asHgwcPhkWLFjFMqJgOHTqAWCyW/uzm5gbLli2DoUOHlljnOY6DwMBAcHZ2ru6Y5XJ0dASBQCBzWbdu3WDChAkwfPhw4PP55f6ODh06qCqewmxtbSE9PV3mMh0dHfD09ITBgwfDoEGDwM7OjlE6xRkaGkJeXh5wHFfi8q5du0KPHj2gR48e0K5dO7X/SPLCwkIoKCgocbmJiQl06tQJOnfuDJ07d4YOHTqo/BO1KyM/P7/EulXMwsICXF1dwdXVFdzc3MDV1RVsbW3V8lNZCwsLITY2tszr69evD87OzjKjRYsWoKenV2UZVNaIGBsbl/i45lq1aoG5uTnzj3Fu2bIl3L17F5KSksDCwgL09PSYf9Z+RfB4PNiyZQsYGRnB4MGDYcyYMRAXFwcbN25UyxVenrFjx8LJkyfByckJvvvuOzA0NJReN3PmTFi2bJlG1OTm5gY9evQAbW1tWL58OXTv3r3M3Nra2mrZhAD82+T27dsX3rx5AxMmTICvv/5aI3bYX9LV1YX+/fvDlStXoH///jB48GDo27evRv6rg549e0JkZCS4u7tDz549oUePHtCxY0fQ19dnHU0pnTp1gr///huaN28ubTo6deoEjo6OoKWlOf+H1dXVFQ4cOKBRTUdpirdBBgYG0Lp1a5mGw8nJqVr+7Um1/q8ZLy8vcHFxgS1btii0fHX9rxmxWKyRjciXlixZAuHh4XDlyhXWUSqE47hSN0SIqDFPagCAgoICmUZKU2VmZoKpqalG/e1Lk5aWBqamplX2PzRYSU1NBSMjI6hduzbrKJWSlpYGPB5P4/+vV0ZGBuTm5mpU01EagUAAycnJ0KxZsyqdTVNm/03/9K4Gefr0Kejp6antq2xCCCH/DcrsvzV/GoBIubm5sY5ACCGEKEVzDsgRQgghpMahRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIUTNFRQUwKtXr0AgELCOUuV0WAcghBCiejExMfDx40fg8/nSYWxsDFpaNeP1aGJiIkycOBFMTEzA2tq61GFlZQV6enqso1aIgYEBrF69Gs6ePQt8Ph8aNWpU5rC0tAQej8c6ssJ4iIisQ5QlOzsb+Hw+CAQCMDExqdTvysjIADMzsypKpn5ycnLA2NiYdQyVKCgogPz8fDA3N2cdpcpJJBIIDw8Hc3NzqF+/Pus4VUIsFkNGRgakp6fDp0+f4NOnT9CqVSuwt7dnHU2uO3fuwMOHD4HH44GWlhbweDyFv+/YsSO0a9eOdQlyffr0Cdzd3SEqKkrmcmNjY2ljYmJiItOoFP/cuXNn6NGjB6Pkijt69Ch8/fXXcpcxNzcv0aB06tQJvvrqK7XfeWdmZkLbtm0hLi5O7nIGBgbQsGFDaWPSsWNHmDx5Mmhra1dTUuX23/+ZGZFVq1bBpEmT1H5jURHBwcGQlJQEI0aMYB2lSonFYjh8+DAcPHgQbt26xTpOlUhNTYVHjx5BSEgIhISEwOPHj2Ho0KFw8OBB1tHK9c8//0BUVBR8+vRJpsko/r74a1ZWlvQ2PB4PVq1aBYMHD2YXXEFubm6wbNkyePLkicK3MTIygrVr10KbNm1UmKxqmJubw6VLl8Dd3V1mej8nJwdycnLgw4cPJW5jamoKq1evhm7dulVn1AobPnw4HD9+HK5du1bmMsXr7evXr6Fu3bqwcuVKGDhwoFo3Ifn5+RAeHg5hYWHQsmXLchuRwsJCePfuHQgEAujXrx+MHTu2WpsQpaEaEwgECAAoEAgq/bt27dqFxsbGeOvWrSpIpj44jkMPDw/cunUr6yhVhuM4vHDhArZs2RIBAI8cOcI6UoUIhUJ8/Pgxbtu2DceOHYtNmjRBAJAZo0aNwqKiItZRFRIeHo42NjYlaihrmJmZ4fXr11nHVkp6erp0vStv9OjRA6Ojo1lHVkhubi7eunULV61ahc2aNSu3Ni0tLZw9ezampaWxjl6mgoICfPz4Me7cuROnTp2KLi4uqKOjo9BjZ2xsjKtXr8bs7GzWZcgQiUQYFhaGJ06cwO+++w59fHywadOmyOPxFH7eAQBaW1vjr7/+inl5ecxqUWb//Z9pRN6+fYsAgHp6enj69OkqSKceLl++jACAfn5+rKNUiaCgIOzcubP0CeXs7IxisZh1LIUkJSXh6dOn0dfXFzt37oz6+vpyNxZDhw5FkUjEOrZS4uLi0MHBodwNYfv27TE2NpZ1XIVwHIfh4eG4ceNG9PT0RG1tbbm1mZiY4J49e5DjONbRy5Seno4XLlzAxYsXY4cOHRTeQQMAenl54cuXL1mXIKMyTcfnQ09PDxctWsS8wZJIJBgdHY0XL17EtWvX4ujRo7F169aoq6urdE1fNiBbtmzB/Pz8aq2H4zhMTU3FoKAg3LdvHy5ZsgT79+9PjciXOI7D+vXrIwAgj8fDHTt2VEFCtiQSCTo5OSEA4OTJk1nHqZSwsDAcPHhwiSfW1atXWUdT2IcPH9Db21uhDcbAgQNRKBSyjqyU169f4+LFi7Fu3bpya/vmm2+wsLCQdVy5CgoK8Pr16zh37ly0s7NTeEM/cOBATEhIYB2/hLi4ODx69CjOnDkTHR0dK7QTa9y4MZ49e5Z5g1WZpkNLSwsdHR2xVq1aJS6fPHkyxsXFVWstHMdhYmIi/vXXX7h582acPHkytm/fHo2MjJRuoJydnXHcuHG4bt26Es/BevXq4datW1XegBQUFOCrV6/w9OnTuHbtWpwwYQJ27NgRTU1Ny8xOjcgXxo0bJ/MH8vf3Z/6kq4yjR49Ka+nXrx/rOBWSlpaGU6ZMQS0trVJfmWna48NxHP72229yNyre3t5YUFDAOqpCBAIB7t69Gzt27FjuxtLQ0FCtD6N9+PAB9+zZg4MHD5a7I9DS0iqxI7OwsMDjx4+rxfrIcRy+fv0ad+3ahePGjcOGDRsqtINu27Ytzp8/H0+fPo0NGjSQXmdkZIRr1qyp9lfRiFXTdEyYMAG3bt2KwcHBmJubi3l5eainpyddzsfHB1+/fq3yWjIyMjAwMBB37NiBs2fPxm7duqGZmZlSDYeWlhY2b94cv/rqK/z+++/x1KlTGB4eLjNzGh8fL9OAbNu2rUofO4lEgvHx8Xjjxg3cvn07zps3D/v06YONGzdW+hARNSKl2Ldvn8wfqH79+rhz584q+d3VTSgUyrySc3FxYR2pQjiOwxcvXuDYsWNLrMCPHj1iHU9pV69eRXt7+zKflD169GCywVdWREQETpgwAQ0NDUut48sddbNmzdRuOh/x30b3u+++w7Zt28rdWNapUwfHjBmDR48exfT0dPTw8JBeN3r0aExNTWVah1AoxE2bNuGQIUPQ3Ny83I2/vr4+du3aFVesWIHXrl2T2YampqZKlxs3bly1z/AcOHCgwk3H119/LdN0lObatWsIAOjp6YkPHz5UWR0XL17ExYsXo7e3t0xjp+iwtbXFfv364ZIlS/Dw4cP47NkzhbYNO3bswPr16+Nvv/1WJS9o7ty5gytXrsSRI0dimzZtlJ6tKR6mpqbYsWNHnDBhAq5duxaPHDlCjUhpoqOjpSs1AKjlhlNRz549w4CAADQyMkI7Ozu0tbVlHalSxowZI7NSDx8+nHWkCgkICCjzidq1a9cyN57q5smTJyXyGxgY4Lhx4/DWrVsyTb2Pjw9mZWWxjlyqzMzMMs/5aN26NS5btgyDgoJkThjmOA6NjY2xXr16ePHiRYbp/w/HcWhpaVnmumViYoL9+vXDn376CYOCguQeGjt//jy6urri/fv3q7GC/1Pe7JoyTUdpDh06hNeuXVP57NXIkSMV2kGbm5ujl5cXzp07F3ft2oXBwcGYmZlZ4ft99OhRlc6o+vr6Ktxs6OrqooODAw4ZMgSXLl2K+/btw6CgIExNTS3x96aTVcvAcRy2bdsWb968iUFBQVXyO1lLTEzE6OhoDAkJUYtp44rKycnBcePG4bhx41BbWxvfvn3LOlKFiEQibNGiBZqbm2PXrl2lT+BOnTqp3Rn68nAcJz3/yNXVFXfs2CGz8VyzZg1qaWnhhg0b1H698/T0lDZS/fv3x4CAALkn0sbExODUqVMrtbNQhWHDhknXJ2traxwxYgRu27YNX7x4odQJ3QkJCSiRSFSYVL7Zs2eX2nRs2bJF6aaDpdWrV8vspGvXro0dO3bEqVOn4pYtW/DmzZuYnJys9s+P3bt3l2g46tWrh56enjhjxgzcvHkzXr58Gd+9e6fUO/yU2X//Zz7QrFhCQgLY2tpWye8iVe/Zs2ewd+9e2LVrF+soFRYaGgq2trZw9OhRmDdvHri5ucHNmzeBz+ezjqaUe/fugampaamfkbFmzRro0qULeHl5VX8wJd24cQNEIhF0794djIyMyl2e4zi1/LTRmzdvQkJCAnTt2hWaNm2q1p97IU9gYCC8ePECXF1dwcXFBWrXrs06UoU8efIEbt26Ba1bt4bWrVtDw4YN1XK9Kc/r16/h5MmT0KJFC2jRogU0b968Sva3yuy//3ONCFFviAgZGRk14lNUDx48CNu2bYNbt27VuE/1VdedNSFEPSiz/6YtCVErPB6vRjQhAABt2rSBGzdu1LgmBACoCSGEVJn/zEe8E1LdauK/EyCEkKpGL2sIIYQQwgw1IoQQQghhhhoRQgghhDBDjQghhBBCmKFGhBBCCCHMUCNCCCGEEGaoESGEEEIIM9SIEEIIIYQZakQIIYQQwgw1IoQQQghhhhoRQgghhDBDjQghhBBCmKFGhBBCCCHMUCNCCCGEEGaoESGEEEIIM9SIEEIIIYQZakQIIYQQwoxKG5F169ZB+/btwdjYGCwtLcHHxwfevn2ryrskhBBCiAZRaSNy7949mDNnDoSEhMCNGzegqKgI+vTpA3l5eaq8W0IIIYRoCB4iYnXdWVpaGlhaWsK9e/egW7du5S6fnZ0NfD4fBAIBmJiYVENCQgghhFSWMvtvnWrKBAAAAoEAAADMzMxKvV4oFIJQKJT+nJ2dXS25CCGEEMJGtZ2synEcLFy4EDw8PKB169alLrNu3Trg8/nSYWtrW13xCCGEEMJAtR2a+eabb+DatWsQHBwMNjY2pS5T2oyIra0tHZohhBBCNIjaHZqZO3cuXL58GQIDA8tsQgAA9PX1QV9fvzoiEUIIIUQNqLQRQUSYN28enD9/Hu7evQt2dnaqvDtCCCGEaBiVNiJz5syB48ePw8WLF8HY2BiSk5MBAIDP54OhoaEq75oQQkgNkZ+fD9ra2jV2xlwoFMK+ffvA3t4eHB0doUGDBsDj8VjHqjYqbUR27twJAABeXl4ylx88eBAmTZqkyrsmhJD/jH/++QdCQkLA2tpaZhgYGLCOViVEIhG0a9cOxGIxNG3aFJo0aQJNmzaVjiZNmpT5bkxNoK+vDxkZGeDt7Q0AAMbGxtCyZUtwdHSUjpYtW0Ljxo1BS6vmfSB6tX6OiLIUPdmlsLAQ9PT0auQDBPDvIa6a3B1TfZpNIpGAtrY26xhy3blzB96+fQt6enqgp6cH+vr6cr9+/r2RkRHUqlWLdQlyCYVC6Nq1Kzx58kTmclNTU5nGpF69eiWalfr164OFhQWj5IoLDg4GT09P4Diu1OtNTU1lGpPPGxVbW1u1fw4WFRVBp06d4NmzZ2UuY2hoCA4ODiWaFHt7e7Xb/6ndyaqqdv/+fZg4cSKkpqaCgYGBdOjr68v9uX379rBgwQLW8ct18+ZN+PXXX8HT0xO6d+8O7dq1Ax2dGvHQAQDA77//Dl9//bXabyiUlZWVBT///DNMmjQJ7O3tWcepkKKiIvj48SMkJCRAfHw8JCQkyAw+nw+HDh2Cxo0bs44qV8uWLWHq1KkQExOj1O369OkDO3bsgKZNm6ooWdXQ19eHM2fOQLt27eDTp0/Sy7OysiArKwvevHlT6u2GDh0Ka9asUetGBBHh48ePUFhYCG5ubvD48eNSl8vKyoJnz57J7Mi/+uorWLFiBTRs2LC64ipEIpHAx48f4f379xATEwMxMTHw/v17yMnJkXu7goICePHiBbx48QJ4PB4MHjwYFi9eDM2bN6+m5GUTiUSQmJgICQkJ8OHDB4iKilL4tjVib9azZ0949eoVzJw5E86cOVPugwkA0Lp1a/jll1+qIV3l9e7dG+Li4mD69OkA8O+0Xbdu3aB79+7QvXt3aNOmjdq/IpXn7t27IBAIYN68eayjVInCwkIICAiAtWvXwoABAzSuCcnJyYGJEydCSEgIJCcnQ1mTpgMGDIDjx49rxFvrra2t4a+//oLOnTtDenp6uctbWlrCli1bYPTo0WrdICcnJ0t3vs+ePQOJRKLQ7by8vGDdunXg7u6u4oSKE4lEEB0dDREREfDmzRvp1zdv3kBubq7Cv0dbWxvGjBkDfn5+4OjoqMLEZUNEyMjIkDYYn3+NiYmBuLg4KCoqqtDvNjQ0hMmTJ8PChQurbdvyZZPx5dcPHz5ASkpKmduKcqEaEwgECAAoEAgUWp7jODx8+DAaGxsjAJQ5jIyM8NWrVypOX/XWrFlTaj3Lly9HiUTCOl6FzZo1Cw0MDDAsLIx1lEoRi8V46NAhtLW1RQBAPT09jImJYR2rQj58+IBt27Yt8zm0ePFiFIvFrGOWi+M4DA8Pxy1btmD//v3R0NBQ7rYBAHDmzJmYkZHBOnoJSUlJePnyZfzhhx9w8ODB2KBBg3Jr+XK0bdsWr1+/jhzHMasjKysLQ0JC8NChQ7hs2TIcMmQItmjRArW1tZWu5/Ohp6eHM2bMwOjo6GqpIz8/H8PDw/Hy5cv422+/4aJFi9DHxwfbtGlT7j6oIsPa2hrXrl2L6enpVVqHUCjEmJgYDAwMxOPHj+OGDRtw3rx56OPjg25ubmhtbY08Hq/CuRXZf9eoRqTY+/fv0cPDQ+4fp06dOlhUVKSi5KrBcRzOnz9fpg5nZ2fMzc1lHa1SFi5ciACA3bp1w8LCQtZxKiwjIwP/97//SR+bhQsXso5UYU+ePME6deqUeN7o6uri/v37WcdTWFxcnMIbzNatW+P9+/dZRy6VRCKp1M6tWbNmeOLECbV4weLi4qJ0fisrK/T09MSJEyeWuM7Q0BAXLlyIHz58qNY6hg4dWuHHg8fjoa2tLXbr1g0nTZqEP/zwAx45cgTPnTtXYlknJyc8ePCgyraNxdvfyg5dXV20s7PDrl274tixY3HBggUK779rxKGZL9nZ2cHdu3dhw4YNsGrVKhCLxSWWGTBggMadZ8Hj8eDXX3+FtLQ0+OOPP8DQ0BAsLS3ByMiIdbRKcXV1hZ9//hnGjx8Penp6rONUWJ06dWDmzJkQFhYG9+/fh2+//ZZ1pApr3bp1icN95ubmcPbsWfD09GSUSnkNGzaE5s2bw7t376SX8Xg8mSlkQ0ND8Pf3B19fX9DV1WURs1xaWlrQrl07uHfvnszlJiYm0K5dO3B1dQU3NzeoV6+ezLsU69WrB/7+/jBlyhS1qa1ly5bwzz//lLhcS0sLmjRpAi1btpSekOng4AAODg5Qp04dAAC4ePEiHD58GAD+rX3OnDmwcOFCsLS0rM4SAACgSZMmcq83MzMDOzs7sLOzgyZNmsh8bdiwYalvRQ4ICJB+7+3tDYsXL4ZevXqp9PCgvA8ZLaarqws2NjZgY2MDtra2Jb63tbWFunXrypwwm52dDVu3blUog2btiZWgo6MD3377LfTp0wfGjx8v3RDVqVMHhg0bBiNGjGCcsGK0tLTg0KFD8OnTJ+jatSvMmzdPrY9hK2L8+PGsI1SZZs2awbVr1+DixYtqfQJgeQwMDODo0aPw559/wo4dO8DR0REuXbpU7sZXHY0aNQoiIyOhT58+0Lt3b3B1dYXU1FQAAOjbty8EBARoRF1eXl7A4/GkTYerqys0bdpUZuNfvJPm8/mwfPlymD9/vtq9UGnbti28efOmRMNhb29f7ueEnD9/HszNzWHhwoUwd+5cMDU1rZ7QpShukj5vMD7/ns/nK/07z58/D1OmTIFFixaV+T/ZqlpxbmWajKpWI96+W568vDz43//+B7t27QIdHR0oKCjQuNmQL+Xm5sKrV6+gc+fOrKOQGmz58uXw8uVLOHHiRIU2rOrmw4cPYGtrC9bW1rB161YYMWKExjfyn5s+fTqYm5vD0qVLNfpzNcpy+PBhGDZsGNSuXZt1lCqHiJCWlsZkdkcVlNl//ycakWKXLl2CqVOnQkhIiEa8AiKEtQcPHkCHDh00vnEvdunSJbh27Rr89NNPTF9Nq0pOTg4YGxuzjkEINSLypKSkQFFRkULHxQghNYtIJNLo85AI0RT/uQ80U4aVlRXrCIQQRqgJIUT9qNdnwhJCCCHkP4UaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwU2MbkYKCAhCLxaxjEEIIkQMRWUdQKUSEyMjIGl1nUFAQJCQkVPj2OlWYhamkpCR48OAB3L9/H+7fvw+GhoZw584d1rGqVGFhIbx8+RKePn0KL168gNWrV0P9+vVZxyKEqFhhYSF8/PgR7OzsQEurZr1+LCgogMGDB0P9+vXB3d0dOnbsCM7OzqCrq8s6WpXg8XiwZcsWOHXqFHTp0gW6dOkCXbt2hbZt29aYGtPS0qBbt25gZ2cHXl5e4OXlBa6urgrfnodq3KZlZ2cDn88HgUAAJiYm0sslEgmEhYVJG48HDx5ATEyM9HoejwdPnjxR6g+hbkQiEYSFhcHTp0+lIzQ0VDrLM2/ePNi2bRvjlJWHiJCWlgZv374FZ2dn4PP5rCMRonYQEQYMGABBQUHg7OwMbdq0kX51cnKC2rVrs45YKWfPnoXhw4dLfzYwMAA3Nzdwd3eXjgYNGjBMWDnp6elgb28PWVlZ0suMjIygU6dO0sbE3d0datWqxS5kJSAieHp6QlBQUInrvtx/l0YjGpEPHz5ARESEtOkICQmB7OzsMm/XqVMn2LRpE5iZmUGdOnWgTp06oKenV43JlSMWiyEiIkLacDx58gRevnwJIpGo1OXr1asHERERGrXTzs/Ph8jISHj37h28ffsW3r59K/1eIBDAgAED4NKlS8Dj8VhHJTWIQCCA8+fPg7W1tXTUrVsXtLW1WUdTWlxcHLRu3Rpyc3NlLufxeNC0aVNo06aNTIPSqFEjjXg+SSQSyMjIgH79+sGzZ8/KXM7GxkY6Y+Lu7g6urq5gaGhYjUnLh4hQUFAAAoGgxDhw4ABcv369zNvq6OhAu3btpI1Jly5dwMLCohrTlyQWiyEvLw9ycnIgNze3xPj88idPnsClS5dK/A5FGhFANSYQCBAAsFmzZggAlRpGRkbYoEEDbN26NXbt2hW///571uUhIuLDhw+xbdu2StWira2NDRo0wHbt2uHUqVNZlyBXREQE9ujRo9yadu7cyTpqhcTHx+O0adNw/PjxOG3aNJw/fz6mpKSwjlVpe/fuxV27dmFBQQHrKJU2c+ZMmXVNS0sLra2tsX///vj27VvW8RTm5+eHtra2Cm8nXF1d8fHjx6xjl+Dn54edOnXC5s2bo5mZGfJ4vApt01u0aIHXr19nVsfWrVvRy8sL27Zti02aNEFzc3PU0dGp9L6qeDRq1AiPHj2KHMeptI7jx49j7969sVOnTujk5ISNGzdGCwsLNDAwqJI6BAJBuRk0ohHJysrC4OBgnDZtGhobG1fJH2fEiBGsy5PiOA7v3r2LY8aMQT09PaXq6NSpE+v45RKLxXj69Gl0c3Mrs44GDRqwjllhMTEx2LVrVwQAtLKyQpFIxDpSpdy+fVv6uFy+fJl1nErhOA4tLS1l1jVTU1Ncv3495uXlsY6nlPbt2yu0TfD29sbLly+jRCJhHblUX331VYW32wYGBjh+/Hi8c+cO8/rmzZtXZU1H8TA2NsYpU6ZUa33r16+v8jqUbUQ04mRVHo8HHh4e4OHhAVu3boULFy7AoUOH4ObNm6WeidymTRswNjaGzMxM6SgoKJBZpk6dOtUVv1w8Hg88PT3B09MT0tLS4PDhw7Bnzx6IjIws97bW1tbVkLBytLW1Yfjw4TBs2DC4e/cubNy4UWaK0tzcHHr37s0wYeU0btwY7ty5Az///DMgosafgNaiRQswMDAAXV1dsLKyYh2nUng8HqxevRpmzZoFhoaGsGDBAli6dKlaPf8VZWNjA0+ePCn1OmNjY5g8eTLMmTMHmjdvXs3JlPPl4QYdHR0wNzcHbW1tSExMLPU2bm5uMHXqVBg9ejSYmppWQ8rylXVo3NjYGPh8fomRlZVV6qEZbW1t6NOnD0yYMAEGDx4MRkZGqo4uQ975Rfr6+lC7dm0wNjaG2rVry4wvL/v06VPFz1tUebtVCcUzImV1VPHx8bh27Vps3ry5TAc2YcKEEssWFhZiUlIShoeH4/379zEiIkLV8SuF4zi8desWjhw5EnV1dWXqmzdvHn78+BGfP3+OYWFhrKNWyD///IPjxo1DbW1trF+/PvNXN1VF02dDihUUFGB8fDzrGFXi/v37OHPmTPz48SPrKJWSkpKC69atk9kWODg44Pbt2zE7O5t1PIW9efMGHz16hFFRUZiVlSU99DB//nyZ2szMzHDBggX48uVLxolLFxUVhYGBgfjy5UuMjY3FzMxMFIvFZS4/a9Ysmfratm2Lv/zyCyYlJVVj6pLi4+Px9u3b+PjxYwwPD8eEhATMzMxUelu2cOFCaW1aWlro5eVVsw7NlFcIx3H44MEDnDFjBpqYmKC+vj6mpaVVU0rVS0lJwQ0bNmDTpk0RANDCwgILCwtZx6oSsbGxuGDBAnzx4gXrKKSGqilNLuK/h2d4PB4OHjwYb9y4ofLzB6pLXl4e8vl85PF42KdPHzx58mSN2cYhImZkZEjPU1y6dCmGhoayjlSlsrKy0NjYGNu3b49btmzBxMREhfffiIga8a4Zhc66/f8KCgrg4sWLYG1tDV5eXqoNWM04joPbt2/D7t27Ydy4ceDj48M6EiGkmiQmJsKvv/4Ks2fPBjs7O9ZxqtTNmzfhwYMHMGnSJGjYsCHrOFXun3/+gfT0dOjevbtGvmOrPHFxcSASicDe3l56mTL77xrXiPxXSCSSGrlCE0II0XzK7L9r1kf0/YdQE0IIIaQmoEaEEEIIIcxQI0IIIYQQZqgRIYQQQggz1IgQQgghhBlqRAghhBDCDDUihBBCCGGGGhFCCCGEMEONCCGEEEKYUXkjEhAQAI0bNwYDAwPo2LEjPH78WNV3SQghhBANodJG5OTJk+Dr6wv+/v7w/PlzaNOmDXh7e0Nqaqoq75YQQgghGkKljcgvv/wC06dPh8mTJ4OjoyPs2rULjIyM4MCBA6q8W0IIIYRoCJU1IiKRCJ49ewa9evX6vzvT0oJevXrBw4cPS72NUCiE7OxsmUEIIYSQmktljUh6ejpIJBKwsrKSudzKygqSk5NLvc26deuAz+dLh62trariEUIIIUQNqNW7Zvz8/EAgEEhHQkIC60iEEEIIUSEdVf1iCwsL0NbWhpSUFJnLU1JSwNrautTb6Ovrg76+vqoiEUIIIUTNqGxGRE9PD1xdXeHWrVvSyziOg1u3bkGnTp1UdbeEEEII0SAqmxEBAPD19YWJEyeCm5sbdOjQAbZs2QJ5eXkwefJkVd4tIYQQQjSEShuRUaNGQVpaGnz//feQnJwMLi4ucP369RInsBJCCCHkv4mHiMg6RFmys7OBz+eDQCAAExMT1nEIIYQQogBl9t9q9a4ZQgghhPy3UCNCCCGEEGaoESGEEEIIM9SIEEIIIYQZakQIIYQQwgw1IoQQQghhhhoRQgghhDBDjQghhBBSQSKRiHUEjadxjUhsbCw8f/6cdQyV4DgOAgMD4dq1a6yjqERiYiKsX78edu3axTpKlUtMTITvv/8e7t27xzoKIWpNjT9Ds0I+fPgAHTt2hH379kFubi7rOFUuMjIS1q9fDx8/flTZfWhEI5Keng4BAQHg4eEBdnZ2oKuryzpSlXr37h2sXLkSmjRpAp6enmX+d2JNVFRUBBcuXIBBgwZBw4YNwc/PD3r06ME6VpVARAgODobRo0dDo0aNYNu2bdCxY0fWsaqERCJhHYHUULm5uTB8+HAICgqqEU1JkyZNwNjYGKZPnw7169eH2bNnw8uXL1nHqjLNmjWDI0eOQMOGDaFv375w4sQJKCgoqNo7QTUmEAgQAFBLSwsBAAEAe/XqpfDtxWIxCgQC/PDhA7558wafPn2Kd+/exUuXLuGzZ89UmLx86enpuH37duzYsaO0NgDALl26lLo8x3GYm5uLHz9+xPDwcHz48CFev34dQ0JCqjm5YiIiInDJkiVoZWUlU1/Pnj0REVEkEmFSUhKGhobi3bt3MSgoiHFixeXn5+P+/fvRxcVFprZRo0ZhZGQk63iV8unTJ1yyZAnu27ePdZQq8fHjR0xMTGQdo0oUFBQgx3GsY1SJQYMGIQCgu7s7nj9/HiUSCetISouMjMRbt25hWFgYBgQEyGwLAAA7duyIBw4cwNzcXNZR5YqNjcWrV6/iw4cP8c2bN5iSkoIikUhmme3bt8vUxufzccaMGfjgwYMy18ni/bdAICg3g0Y0Ip+PwYMH47Jly3DOnDk4ceJEHDZsGPbp0wc7d+6Mzs7O2KRJE6xbty4aGhqWuO3nY+rUqdVeT2FhIZ49exaHDBmCurq6peZq06YNDh48GD09PdHFxQXt7OzQzMwMdXR0Sl2+f//+1V5HWXJycnD//v3YuXPnMv/uxsbGaGJiUuJyNzc31vHLFRsbi8uWLUNzc/My62vcuDHrmBWSm5uLa9euRT6fjwCAkyZN0vid3sePH9HGxgYBAC9fvsw6TqWdOXMGR40ahRkZGayjVIq/vz9aW1vLPG9atGiB+/btw8LCQtbxFPbDDz/I3cd8vtOeM2cOvnr1inXkUu3cubPU3LVq1UIbGxt0cnJCNze3Mutr3rw5/vTTT5iQkCDze2t0I1JVY+TIkdVSA8dxeP/+fZw1axbWqVOnyuvw8PColjrKq2/KlClYq1atCtehrjtwjuPw1q1b6OPjIzMzV9bQ1dXVqFd3IpEId+zYUWLHwOPx8OPHj6zjVUpSUpK0ni1btrCOU2m9evVCAEAbGxu8ffs26zgVNmDAgDKfP/Xq1cMNGzZgVlYW65jl+uabb5TeznXq1AkPHTqE+fn5rONLrV27tkr2RTweD3v37o3Hjh3DvLw8pRoRHajB9PT0oHbt2mBsbAy1a9eWDmNjY2jfvr3K7z8wMBDmzp0LoaGhVfL7TExMgM/nywwnJ6cq+d0VERoaCrNnz4bg4GClb6unpwcWFhbS0bBhQxUkrJy4uDhYsGABXLx4UaHljY2NYfLkySAUCsHQ0FDF6SovPT0d/Pz8IDg4GAoLC2Wu69ChA1hYWDBKVjWsra3hypUrEBkZCfPnz2cdp1JEIhF0794dnJ2dobCwEI4fPw7Gxsbg5ubGOprS/Pz84N69e6We2JmUlAR+fn5w4sQJ2Lx5M3Tv3p1BQsW0aNECevXqBcnJyRAXFwc5OTnl3ubhw4fw8OFD+O677+DXX3+FYcOGAY/Hq4a0ZWvSpAkMHDgQMjMzZcaX24TyICLcuHEDbty4AXXq1IGVK1cqfFseovqeLVT8b4Q/16lTJxg2bFiJxuLLn2vVqgV6enqMkv8fkUgEz58/h6CgIAgKCoLg4GDIzMwsc3lHR0fYsGFDiYbD2NgYtLW1qzG5YhARoqKiICQkBEJCQuDRo0fw8uVLEIvFpS5vZmYGYWFhYG1tzfwJqKjc3FwIDQ2Fly9fSkdoaGipG9IrV65A//79GaSsvMLCQkhJSYHk5GRITk4GZ2dnsLOzYx2L1DBLliyBTZs2gYWFBTRv3hxatGgBLVq0kH7ftGlT0NfXZx1TYRKJBDp37gyPHz8u9XoDAwNwcXEBNzc36XBwcFDL7fnnCgsLpU3J5s2b4cCBA2Uua2JiAp06dYLOnTuDh4cHdOjQARAR+Hw+CAQCMDExkXtfGteIWFhYQGRkJJiamrIJVUkcx0FERIS0KQkKCoL4+HiZZYKDg8HDw4NRwsrLz8+H58+fyzQnHz58kF6/ZMkS2LhxI8OElcdxHMTExEgbk1evXsHLly9BIpFAaGhouU88Qv6LOI6DJ0+egL29PZiZmbGOUyV27twJs2fPBgAAXV1daNOmjUzT4ejoqNHv9ExNTQV7e3vIzs6WXtakSRNp09G5c2do1apVicaqeP9dYxqR8+fPw5MnT+Du3bvw+PFjWLRokcbvyD4XHx8vbUqCgoLAyMgIQkJCQEtLI95drZAPHz7Ao0ePICQkBJ4/fw779u2rka+2BQIBAECJBpoQUvMIhUL49ttvoVmzZuDm5gZOTk4aNZujiNmzZ8Pz58/Bw8MDPDw8oFOnTlCvXr1yb1fjGpHPC8nLy4Pnz59Dly5dNGZqX1kZGRlgZGQEBgYGrKMQQgj5DxMKhRVqrpRpRDTuZNVatWpB165dWcdQqZoyZUkIIUSzVccMT82Z+yeEEEKIxqFGhBBCCCHMUCNCCCGEEGaoESGEEEIIM9SIEEIIIYQZakQIIYQQwgw1IoQQQghhhhoRQgghhDBDjQghhBBCmKFGhBBCCCHMUCNCCCGEEGaoESGEEEIIM9SIEEIIIYQZakQIIYQQwgw1IoQQQghhhhoRQgghhDBDjQghhBBCmKFGhBBCCCHMUCNCCCGEEGaoESGEEEIIM9SIEEIIIYQZakQIIYQQwgw1IoQQQghhhhoRQgghhDBDjQghhBBCmKFGhBBCCCHMUCNCCAEAgIKCAtYRCCEMCIVCePbsGbP7p0aEEAVlZGQAIrKOUeUKCgrgu+++g61bt7KOUmUQEW7cuME6BiEaQU9PD/r16wfr1q0DiURS7fdPjUg1ysjIgJycHNYxVEIoFMLevXtrZH15eXnw008/gY+PD/B4PNZxqtSNGzfAyckJ1q5dC05OTqzjVAmRSATTpk2DzZs3s45Carg3b97A27dvWceoNB6PB40aNYIVK1aAl5cXxMbGVuv961TrvVWToqIiSEpKgg8fPkBCQkKpXydNmgRr166tljzR0dGwZcsWuHTpEkRGRip1W0SE9PR0iImJgZiYGHj//r3M971794Zdu3apKHn58vLyYO/evbBp0yawsrKC6dOny10+Pz8f3r17B2/evIGIiAjp15YtW8LJkyerKbViRCIR7Nu3D1avXg0pKSng6+srcz3HcRAZGQnPnj2Dp0+fwrNnz4DP58Off/7JKLHiUlNTwdfXF44dOya9rF69enD48GH4+++/IScnRyPq+FJ6ejoMGzYMAgMDoWfPnnD48GGYOHEi61iVcvXqVejatSsYGxuzjkI+k5OTA69evYIlS5bAgwcPoEGDBqwjVUhMTAzMnj0bcnNzAQAgODgYnJ2dISAgAMaPH18tL740rhEpbjKKG4rSmozk5GTgOE7u71F1x4eI8ODBA9i8eTNcuHABEBFmzZoFurq6JZbNy8uD2NjYEk1G8ffFK0hpWHXjAoEAAgIC4Ndff4X09HQAAJg1a5b0+rS0tBLNxps3byAuLq7UwxtCobDaspeH4zg4ceIErFy5Et6/fy+9vEmTJnD8+HFp0/HixYsSM0DGxsbAcRxoaannZCPHcbB//35YunQpZGVlyVzn6uoq/V5LSwsyMzOhTp061Zyw4sLDw2HQoEHSx+zWrVtw69YtaN++PTg6OjJOVzFisRh8fX1BV1cX1q1bBwMHDmQdqcIQEQoLC+Gnn34CExMTWLJkCetIlfLdd9/Bzp07oaioCPr27QuBgYEa9Xwpdvr0abh+/brMZTk5OTBhwgS4fPky7Ny5E8zMzFQbAtWYQCBAAMDBgwdjhw4dsH79+qilpYUAUOnh6empksxFRUV48uRJ7NixY4n7XLt2Le7btw9XrFiBY8aMQXd3d7S0tKxUHY0bN1ZJHWVJS0vDb7/9Fvl8foksffr0QQ8PDzQ3N1e6Dh0dHRSJRNVay5c4jsOrV69imzZtKvWYREZGMq2jLGFhYejh4aFwHefPn2cdWWFXr15FExOTEjXUrl0bT5w4wTpehe3Zs0day6BBgzAqKop1pEqZOXOmSre/1WnUqFEy65qHhwfm5eWxjqU0Ly8vuduBBg0a4M2bN5X+vcX7b4FAUO6yPET1PfsuOzsb+Hy+0rfT1taGBg0agI2NDdja2pb61crKCrS1tassa05ODuzbtw+2bt0KcXFxVfZ7AQDMzc3Bzs4OmjRpAnZ2djLfN2zYEPT09Kr0/kqTmJgImzZtgt27d0N+fn6Ff4+enh7Y29tDy5YtwcHBARwcHKBly5bQvHlzqF27dhUmVs7Dhw9h+fLlEBgYqNTtbGxswM3NDVxdXaXD0tJSRSkrpqCgAH788Uf4+eefQSwWl7mcrq4u9OzZE/r06QN9+vQBR0dHtT8nBhFh27Zt4OvrW+osqLm5OVy4cAG6dOnCIF3l5Ofng729PSQmJoKFhQWsXLkSZs6cCfr6+qyjVVhubi64uLiAhYUFhISEsI5TYUeOHIGpU6eWeD4NHDgQzp8/Dzo6mnOwISsrC1xdXWVmf0uzePFiWLt2rcLrX/H+WyAQgImJidxlNa4RYdFkyJOQkADbtm2DPXv2QHZ2doV+h4GBQYkG4/Omo7wHUZViYmJgw4YNcPDgQRCJRArfztTUVNpsfN502NnZqdWT9PXr1/Dtt9/CxYsXy13WwMAA+vbtq9ZNx5f++usvmD17drkbGYB/D8ecO3cOhgwZUg3JKq+oqAjmzp0Le/bsKfV6HR0dsLGxgWbNmsHevXuhcePG1RuwktavXw9r1qyBxYsXw+LFi5luB6pSSEgIzJ07F54+fco6SqUkJibC3bt34c6dO3Dnzh2Ijo4GAIDJkyfD/v371b6JB/j3RYqPjw/8/fffCi3v5OQEx48fh9atW5e7bI1rRI4cOQLNmzcHW1vbam0y5Hn27Bls3rwZTp06pfDbnWxsbKB3794lmg5ra2u1W2kjIiJg3bp1cPz4cYXrs7Kygj/++AMcHR3B0tJS7Wr6XFxcHPj7+8ORI0cUfksuj8eD69evQ58+fVScrvKSk5Nh0aJFcOLECaVuZ2BgALdu3YLOnTurKFnVyMrKgrlz50JkZCTY2tqCra0tNGzYUPq9Om0rKiI7Oxs2bNgA8+bNA2tra9ZxqtzJkydh1KhRrGNUqfj4eGlT0rFjR/jmm29YRyrXn3/+CdeuXYPCwkIQCoVQWFgoHWX9DADg7+8Pc+bMkXsuXI1rRBQppLqlp6dDREQEhIeHQ3h4uPT7jx8/lnkbU1NTCAsL04izq3NyciAmJgaio6Ol4/379xAdHQ1xcXFlTvFv3ry5xLtL1JFQKITU1FRITk6WGUlJSSV+Ln7yAfw71f/s2TNo1KgRw/Tl4zgOioqKQCgUgkgkKvNraZfVrl1b7WdFEFGtG93Kqun11XT/hcevvBqpEWFIIBBARESETJMSHh4ufZdOv3794MqVKxq9korFYkhISCjRoERHR8OHDx/gxo0b4OLiwjpmlUBEyMnJkWlO6tatC927d2cdjRBC1BY1ImooLy8P3r59C+Hh4dCzZ0+oV68e60gqgYggEok0+oQ6QgghlaPM/lslH3YQGxsLU6dOBTs7OzA0NISmTZuCv7+/Uic71jS1atWCdu3awfjx42tsEwLw73kU1IQQQghRlErevvDmzRvgOA52794NzZo1g7CwMJg+fTrk5eXBpk2bVHGXhBBCCNFA1XZo5ueff4adO3cq9DbCYjXp0AwhhBDyX6HM/rvaPtBBIBCU+zGxQqFQ5qO+K/q5HIQQQgjRDNXyDzGioqLgt99+g5kzZ8pdbt26dcDn86XD1ta2OuIRQgghhBGlGpHly5cDj8eTO968eSNzm48fP0Lfvn1hxIgR5f5nVj8/PxAIBNKRkJCgfEWEEEII0RhKnSOSlpYGnz59krtMkyZNpP/7JDExEby8vMDd3R0OHTqk9H8kpXNECCGEEM2jsnNE6tatC3Xr1lVo2Y8fP0L37t3B1dUVDh48qLb/Fp0QQggh7KjkZNWPHz+Cl5cXNGrUCDZt2gRpaWnS62ri/00ghBBCSMWopBG5ceMGREVFQVRUFNjY2Mhcp8Yf5EoIIYSQaqaS4yWTJk0CRCx1EEIIIYQUoxM3CCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCiBoqLCyEv/76i3UMQlSOGhFCiEYTi8WsI1Q5oVAIw4YNgytXrrCOUiVEIhFkZmayjkHU1H+mEcnIyICHDx/C4cOHYcWKFXD58mXWkSpEIpFAZGQknD9/Hn788Uc4efIk60gVlpOTA4GBgfDrr7/CoUOHWMepMESEqKgoOHjwIOzbt491nFJJJBKFlisoKICrV6/C/v37VZyoaoSGhsKMGTNKve7Nmzfwxx9/VHOiyisqKoJRo0bB1atXIS8vD/Lz8+Hu3busY1XK7t274dSpU6xjEDnev3/P7s5RjQkEAgQAFAgECi0vFAoxPDwcz58/j+vXr8cpU6agh4cHWlhYIADIjJkzZ6o4feVwHIcJCQl47do1/Pnnn3HixIno6uqKhoaGMnUMGTKEdVSFZGdn47179/CXX37BcePGoYODA/J4PGkdHTp0YJaN4zh89+6dwsuLxWJ88eIFbtu2DUeMGIHW1tbSOho3bqzCpMrLz8/HZcuW4eXLl8tcJj4+Hnfu3IkDBgyQrl98Ph9FIlE1JlXe77//joaGhjh8+HDpZTk5Obh//37s3LkzAgDq6+tjRkYGw5TKKSoqwuHDh0vXJwcHB7SxsUEDAwOMj49nHa9CBAIBWlhYYKdOndDHx0ep55o6unPnDiYkJOA///yDRUVFrONU2suXL/HcuXPYqlUrTE1NrbLfq8z+W+MaEY7jMDExEe/cuYO7du3CRYsWYf/+/bFZs2aora1douEoa3h5eVVZzqKiIvz7778rfPv09HS8e/cubt++HWfNmoUeHh7I5/MVqqNp06ZVVkdZgoODcdWqVQovX17TUdrQ19dnsuN79eoV9ujRA3/44YcylykoKMDAwEBcu3Yt9uvXD01MTOTWkpCQUI0VlC0wMBCbN2+OAIDv37+XXi4WizE4OBj9/PzQycmpzDru3r3LMH3ZCgsL8ZtvvpHmnDdvHgYHB+OUKVOwVq1aJeoICAhgHVkhYrEYx44dW+bjMWHCBNYRK+T777+XqcPBwQHFYjHrWBXWv39/bNSoEQIA+vv747lz51hHqrCcnBzk8/nS7fOpU6eq7Hcr04joVGwepXqtX78e4uLi4O3bt/Du3TvIyclR+neYmJhAixYtoHnz5tCiRQto27ZtpXOJxWI4evQorFmzBvr06QO9e/eWu3xubi6Eh4dDWFgYhIaGQlhYGISFhUFycrJS99uwYUNo3bo1tG7dGpydnStTglyhoaHw7bffwqVLl2DDhg2lLpOTkwMvXryAZ8+eScfbt28BEcv9/Xp6euDk5ASurq7g5uYGEokEdHV1q7qMUn369An8/f1h586dwHEcfPvtt9LrBAIBPHjwAIKCgiAoKAiePHkCQqFQ7u+zsLCALl26QNeuXcHAwEDV8eXKyckBPz8/CAgIAAAAY2NjMDExgT/++AMuX74M169fh4yMjDJv7+zsDAMGDAAbG5vqiqyw+Ph4GDFiBDx+/Fh62e7du+G3334rsayenh589dVX0K5du+qMWCEcx8G0adPg+PHjpV7foEED6NmzZzWnqrzk5GTYvHmzzGWmpqZw9epV6NOnD+jr6zNKVnHW1tZw9epVAADYuHEjREdHM05UMXfv3oVRo0aBQCCQXnb79m0YMWJE9YepsvZHBYo7KkWHtrY22tvb48CBA3Hx4sW4e/duvHv3LiYlJSHHcVWWSyQS4YEDB7BJkybS+7569ar0eqFQiC9fvsRjx46hn58fDho0CO3s7JSqBQDQwsICu3fvjvPnz8c9e/bggwcPMCsrq8rqKMv79+/x66+/lpnFePHiRYVmOoqHnp4eurq64owZM3DPnj347NkzFAqFKq/lS0VFRbh9+3Y0MzOTyXfw4EGcN28euri4oJaWVrn1NGrUCMePH4+7d+/G8PDwKl2/KuP69evYsGHDEs8LeTUZGhriwIEDcdeuXWo9/f/XX3+hubl5uY+Ni4sL/vbbb/jp0yfWkRXCcRzOmDFDbk2TJ0/G3Nxc1lGVNnv27FLrGTZsGEZGRrKOVyErVqyQ1uHn58c6TqVcvnxZ5nB/ixYtqux317hDM18OS0tL7NKlC06dOhU3btyIFy9exIiICJXv2EQiEe7fv7/UpmLFihU4cuRIdHR0RB0dHaUaDmNjY+zUqRNOnz4dt27dirdu3cKUlBSV1lKalJQUnD9/Purq6pbI2Lx5c41rOr508+ZNbNWqldINIQBgq1atcNasWXjs2DG13Fl/+vQJJ06cqHA9jRo1wjlz5uDVq1cxPz+fdXy5JBIJrl69Wu76Z2JignPmzMHnz5+zjqsUjuNw7ty5Cj1mzZo1w/v377OOrLDIyMgS20JPT08MCQlhHa1Stm3bhgCAderUwczMTNZxKu3+/ftYp04d6WP08ePHKvm9Na4RWbx4MR4+fBhDQkKYnHgmEolw3759FZrV+Hzo6+uji4sLjh8/HtevX4+XL1/G2NhY5q+mBQIBfv/996UeX9fUpuNz0dHROHToUIVr0tHRwY4dO+L//vc/vHjxIqanp7MuQa6zZ8+ilZWV3Jq0tbWxa9euuGHDBgwLC2O+zinq06dP2K9fP4Wa+du3b7OOqxSO49DX11duXYaGhti1a1dcsmQJnj17tsp2EtVh1KhR0jqcnJzw6tWrGrPeyXP69GkEANy4cSPrKFUmLCwMGzRogACAx44dq5LfWeMaEUXfNVPVhEIh7t27Fxs3bqzUzllLSwtbtGiBw4YNQ39/fzx9+jS+efNG7c6wLigowF9//bXUdxVpatPxuZycHPTz80M9Pb1ya7OwsMBVq1bhrVu3NGYKPDk5WeYdFuXtqJ8+fco6slKePn0qPSlQ0fXz7NmzrGMrhOM49PPzK3XWY/z48bh9+3Z8+vSp2r9zqSxPnjxBgH9n3o4cOaLRJ6d+KSgoCOvXr6/2M4nKiouLQwcHB5w2bVqV/L4ad7JqdROJRHD48GFYu3YtxMXFKXSbtm3bwqJFi8DJyQkcHByYn7Aoj0Qigd9//x38/f0hPj5eods0bdoUXrx4AcbGxipOV3kcx8GxY8dg2bJlkJSUpNBt0tPTwcnJCXr06KHidJWHiHD06FFYuHCh3JNOP5eTkwN9+/aFoKAgcHBwUHHCykFE2L9/P8ydO1d6krCenh6Ym5uDubk5WFhYlPrV3NwcrKysABGBx+MxrkK+1atXw/bt26FXr17g7u4O7u7u0LFjR7CwsGAdrdIQETZt2gS//vorfPPNNxp5Qqo81tbWsGrVKjA0NGQdpUo1bNgQgoKCYOHChdV+3zxEBd7ewEh2djbw+XwQCARgYmJSbfd77do1uHfvHsTFxUFcXBzExsaWu0PT09ODkJCQKnk3jqo9fPgQ7ty5A0lJSZCcnCwzcnNzy7zdN998Azt27KjGpBUTHh4Ot2/fBoFAIB3Z2dkyPxePz9+BZWRkBEFBQWr/Lov4+HgICgoCjuMAEaVfP/++rOtsbGzgq6++Yl2CXJ8+fYKnT5/KNBm1a9dW++ZCUXl5eRAbGwsODg6gra3NOk6VEwqFUFhYCHw+n3UUlRAKhaCtrQ06OjXzdXxeXh4YGBhUet1UZv9NjYiChEIhJCQkSJuTL0dCQgLY2dnBs2fPNGLWoCy5ubklmpPk5GRp0/Ldd99Bp06dWMesMhzHQU5OjrQx0dPTgxYtWrCORQghGo0aEQYkEgkkJSVBrVq1oE6dOqzjEEIIIcwos/+umXNLDGhra6vlB0ARQggh6uw/80/vCCGEEKJ+qBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQggpR0ZGBhw/fpx1jBrpP9eIiMViCA8Ph7i4ONZRKgURISYmBqKjo1lHqbTU1FSIiopiHaPS8vLyakQdYrEYYmJiWMeoNESEpKQk1jGqRHZ2NusISkHEUi8Xi8XVnKTqrF+/Hvbs2cM6RpUQiUSsI8io0Y1ISkoK3LhxA3755ReYNGkStGvXDmrXrg2tWrWC3bt3s46nsOKm48yZM+Dn5we9e/cGCwsLaNKkCaxdu5Z1PKVIJBJ49eoV7Nq1CyZOnAj29vZgZWUFvr6+rKMpTSgUQmBgIPj7+0PXrl3B1NQUvv76a9axKiQ7OxtOnz4NX3/9NVhaWkLfvn1ZR6qwDx8+wPr166FVq1bg6uqq0Tu/kJAQGDp0KDRv3hwKCgpYx1HY8uXLZZoRsVgMv/zyC7Ru3VrjmioAgISEBNi2bRsEBgbCgwcPYOzYsZCbm8s6VoUtWLAAEhMTITY2FiQSCes4AKhihYWF2KZNGwQAfPHihVK3FQgECAAoEAjkLldQUIDPnz/HQ4cOoa+vL/bq1QstLS0RAMocAwYMqERVqsNxHL5//x5Pnz6Ny5cvx169eqGZmVmZdTg7O7OOLFdWVhb+9ddf6O/vj71790ZjY+NS6zA3N0eO41jHlUssFuPjx49x/fr12Lt3bzQ0NCxRh7a2drnrq7qIi4vD7du3Y58+fVBXV7dELW/evGEdUWG5ubl45MgR7NWrF/J4PJk6rl+/zjpeqRISEjAuLq7E5RzH4dWrV9HT01OmjoCAAAYplbd161YEAExPT0dExBcvXqCrq6u0jrlz5zJOqLzJkydL8+vo6CAAYJcuXTAnJ4d1tApxdnZGV1dXtLe3x8aNG+Ply5er/D4U3X8jIuqorMP5/5YuXQr169eHly9fVvp3ISJ8+PABXr16JTPevn2rVFfXtGlTsLGxqXSeykJEiI2NhWfPnsGzZ8/g6dOn8Pz5c8jIyFDo9paWltC4cWNARODxeCpOWz5EhKioKHjw4IF0vH79usxp2mJGRkbg5OQEWVlZUKdOnWpKWz5EhPDwcLh16xbcvn0b7t69CwKBoMzleTweuLi4QGJiIpiYmFRjUsVwHAfPnz+HP//8E/7880+5z0k7Ozv4+PEjtGjRohoTlnTv3j3w9PQs9TqO4+Du3btw5MgROHPmDOTl5ZVYhs/nw4cPH1QdU2lhYWHQr18/+PPPP6Fhw4YA8O+swalTp2Djxo0lHhsej6cRh/3+/PNPWLhwIQAAREZGwsaNG2Hz5s0y2+dHjx6BUCgEfX19RimV8/r1azh8+LD05+IZtufPn0NERAS0b9+eVbQKS0hIgMzMTOnPN27cgOjoaHBxcYFu3bpVf6Aqb4M+c/XqVXRwcMDXr19XakZkxowZ2K1bNzQ1NZU7y/Hl4PP52LVrV5wzZw7u3r0bHz58yKyD/XKmo3fv3nJnOr4clpaW2K9fP/zuu+/w/PnzGB8fz3wGIS8vD+/du4fr1q3DQYMGoYWFhUK1NGrUCMeMGYPbtm3Dp0+fokgkUllGjuMwOTlZ4eWjo6Nx7969OGbMGLSysiq3FkdHR5w7dy6eO3cOMzIyVFZHaTiOwwMHDmBYWFiZyxQUFOCVK1dw5syZWL9+/TLr4PF46O7ujj/99BOGhYUxX7cKCwtxzpw52KFDhxLXRUREoJ+fH9ra2pZai7a2Ng4YMABPnjyJBQUFDNLLd/fuXem27PXr15iXl4fbt2/Hxo0bl6hFT08Pp0+fjm/fvmUdu1xPnz5FIyMjafYvZz+NjIxw8+bNWFRUxDqqUgYPHlzmbPTRo0c1Zga0WG5ubpnbsqqsRZkZEZU1IsnJydigQQN88uQJxsTEKNSIFBYWokAgkI6EhASFdmza2tro6OiIo0ePxp9++gkvX75cZTtqgUCAQUFBSt1GU5oOjuPwzz//xCNHjii0fHx8PJ44cQLnz5+P7du3l05Ryhu6urro7u6OixYtwtOnT+OHDx+qvI6yvH79Gr28vPDMmTNlLpOYmIjHjh3DKVOmlLoj+HI0btwYp06diseOHcPExMRqq+VLCQkJ2K9fPwQAzMrKkrkuNTUVDx48iEOHDpXZMXw5DA0NcciQIbh//36lmjVVi4qKkk7lDxs2DBER09PTcfv27dihQ4cy63FxccFffvlFrWr50qlTp1BPT0+aefbs2Vi3bt0StRgbG+PSpUuZrmPKiI2NRWtr6zIfG29vb3z//j3rmEoLCgoqd5tgb2+P7969Yx1VYRERESVqsLCwwOjo6Cq9H+aNCMdx2LdvX/zxxx8RERVuRPz9/ct90OvWrYu9evVCX19fPHToED5//lwlr3oKCgrwl19+QXNzczx06FCZy2lK0/Glf/75B3v27IkAgH///XeJ60UiET5+/Bi3bNmCI0eORBsbG4Xr8fHxwY0bN2JwcDCTV6Q5OTm4dOlSaaMUHx8vvS4jIwPPnTuHc+fOxZYtW5Zbj5WVFY4ZMwb37t2rFhtSjuNw//79aGJiggCANjY2yHEchoeH4/r167Fz584lzpH4fFhbW+P06dPx0qVLmJ+fz7qcEs6cOSOtDQCwa9euOHTo0FLPYSmuZ/Hixfjy5UvW0cu1detWuY9N8fq2bt06zMzMZB1XYVlZWdiqVatS69HS0sKDBw8yn2GrCI7jsHPnzmU+VnXq1MFNmzap5aybPH///XeJF4uBgYFVfj8qa0SWLVtW7oY7IiICt27dih4eHigWixFR8UakrBmRNWvW4N9//10tr3SKiorwwIEDMtO+xa/iNbXp+FxSUhJOnTpVukHU0dHB3NxcTE1NxYsXL+KyZcuwa9euaGBgUG49Wlpa2KZNG/zmm2/w999/x+joaKYbHI7j8OzZszKPnZmZGV67dg2XLFmCrq6u5e4ITE1N0cfHB7dt26YWhyg+Fx8fj3379pXJa2Zmhs2aNZNbk5OTE3777bf46NEjlEgkrMsoVWFhIc6bN0+h55GBgQGOHj0ar127phHT/BKJBJcsWSK3pqZNm+Lu3bs1bqcmEomwV69ecmtzdHTEO3fusI6qtAsXLpRaj6GhIS5fvlyjmsXP7d+/X6aegwcPquR+VNaIpKamYkREhNwhFApxyJAhqKWlhdra2tIB8O8hlAkTJqikkMriOA7Pnz9f4lWyqampxjYdn8vPz8c1a9ZgrVq1SmzU7e3tFarJ1NQU+/bti6tXr8abN29idnY2s3q+FBkZWWInrcgwNDTEPn364IYNG/DJkyfS5lmdcByH+/btk5kpkDd0dHSwZ8+euHXrVrWYxSlPdHQ0urm5lVtX165dcd++fSUORakzoVCI48aNk1uXh4cHCoVC1lGVxnEcTpkyRaF10snJCe/fv886ssKKiorQ0dGxxAuv6dOnV+vhZVX4/MjDkiVLVHY/zA/NxMXFYWhoqHT89ddfCAB45swZTEhIUPj3VFcjcufOHezYsaPSOzF1bTo+J5FI8NixY2We2CdvtGjRAidPnox79+7F169fq+Wr6fz8fPT390d9fX2FatLV1cWuXbuiv78/3rt3DwsLC1mXIFd8fDx6e3sr1CSOHTsW//jjD416pXbu3Dnk8/lya7O1tcXIyEjWUZUmEAikhz/LG3369JG+3VVTrF27tsx6+Hw+Dh8+HPft26fUNl9dfDlrMHToUAwPD2cdq0oUN4+DBg1S6Qsv5o3IlxQ9NPMlVTciz58/V2gjrylNx5eCg4Plntz3+TAyMkIvLy9csWIFXr58WSM2ileuXMEmTZqUW5u1tTUuXboUr1+/jrm5uaxjK4TjONy7d2+Zn7vy+ahfvz6mpaWxjqwUoVCICxYsUPh5N3r0aJW+u6qqJSYmSj8/Sd4wNDREZ2dnHDZsGO7Zs4d1bIUdP368RC2urq747bffYnBwsEYcMitLfn4+NmjQAAH+/ayQBw8esI5UpXr37o1OTk4qn9GmRqQckZGROHr0aIU3gl26dFH7puNz79+/x5EjRypcX9u2bdV+ZuBzcXFxOHToUIXrMzAw0Khp4bi4OOzTp49SDXLnzp01psmKiYnB9u3bK1SXoaEh1qtXD1u2bIlr165lHV0hERER2KhRI2kNurq62KJFCxw0aBD6+vrirl278NatW5iQkKCWs4zlCQwMRD09PTQ3N8exY8fikSNHMCUlhXWsKrNhwwZs1aoVXrp0SSO298ry9PTE2NhYld+PMvtvHmI5nzbFUHZ2NvD5fBAIBFXyAVGICCdPnoQ1a9ZAQkKCwh81bGhoCI8ePQInJ6dKZ1C1mzdvgr+/PyQlJUFGRobcD+D63P/+9z/4+eefVZyu8p4/fw4rV66EtLQ0KCgogPz8fMjPz5d+X1RUVOrtzM3N4eHDh2Bvb1/NiZUTHR0N33//PeTk5ACPxyt3aGlpSb/v1asXTJ48mXUJcqWkpMCaNWsAEcHU1FQ6+Hy+zM/Fl+np6bGOrJTs7Gz45ZdfwNzcHOzt7aF58+bQsGFD0NFR+WdHVguhUAj79u2D9u3bg6urK2hra7OOVKU4joNLly7BwIEDa1xtxV69egXOzs4qvx9l9t//qUbkS/n5+ZCSkgLJycmQnJwMSUlJ0u+/HI0aNYKnT58Cn8+v8hyqJBaLISsrCzIzMyEjI0M6SvvZ398f3NzcWEeuFLFYXGqDkp+fD2ZmZtC6dWvWEQkhpMajRqSKISJkZmaCrq4uGBsbM8tBCCGEaAJl9t81Y75QxXg8HpiZmbGOQQghhNQ4WqwDEEIIIeS/ixoRQgghhDBDjQghhBBCmKFGhBBCCCHMUCNCCCGEEGaoESGEEEIIM9SIEEIIIYQZakQIIYQQwgw1IoQQQghhhhoRQgghhDBDjQghhBBCmKFGhBBCCCHMUCNCCCGEEGaoESGEEEIIM9SIEEIIIYQZakQIIYQQwgw1IoQQQghhhhoRQgghhDBDjQghhBBCmKFGhBBCCCHMUCNCCCGEEGaoESGEEEIIM/+JRqSgoAAePXoEO3bsgKlTp4KLiwts27aNdSylISLEx8fDqVOnwNfXFzp16gSrVq1iHatCCgsLITAwEH788Ufo3bs3LFy4kHWkCouJiYE9e/bA8OHDYerUqazjVFhhYSFcuXIFZsyYAWPGjGEdp1LevHkDK1euhOHDh7OOUin5+fmwd+9eGDFiBCAi6ziVcv/+fZg6dSpIJBLWUSolPT0dvv/+e42vAxHh7Nmz6rFeoRoTCAQIACgQCBS+TX5+PoaEhGBAQABOmTIF27Rpg9ra2ggAMmPMmDEqTF418vLyMDAwEDds2IBDhw7FevXqlajDy8uLdUyF5OTk4N9//43ffvstdu3aFfX09GTqaN68OeuIChMIBHjhwgWcPXs2NmvWTKYOPp+PRUVFrCMqLCMjA3///XccNmwY1qpVS1qHtrY2fvr0iXU8pSQnJ+OWLVvQzc1N5jGJiIhgHU1pMTExuGTJEqxTp460jlu3brGOVSEvX77EgQMHSuv4/fffWUeqsMuXL6OVlRUCAK5fv551HKWEhoZKv+c4DufOnYsAgHPnzkWO46r8/pTZf2t0I/Jl0+Hs7Fxq01HaaNmyZTVXIx/HcRgZGYlHjhzB2bNnY7t27RSqpXbt2igWi1nHLyEzMxMvXbqES5YswQ4dOihUS0pKCuvYpSoqKsKHDx/i6tWrsUuXLuXW8ujRI9aR5YqNjcWtW7dijx495NZy/Phx1lHLlZubi8eOHcN+/fqVWcuqVatYx1QIx3F4+/ZtHDp0KGppaZWoY9SoUawjKiU6OhrHjRuHPB5Ppg4HBweV7PiqSmnZcnJycPr06TJ16OvrY2JiIoOEyvv777/R29sbEWWbkOJx9OjRKr/PGtmIVKbp0NLSwtatW+PEiRPxt99+wwcPHmBeXh7z2m7cuIE//vgjDhgwAM3NzRWqpU6dOtivXz9cvXo1/v3335iZmcm0jmIpKSl45swZnD9/PrZp06bExqe04eTkhHPnzsVTp05hUlIS6xJkvH//Hnfv3o3Dhg1DU1NTuXUYGxujj48PBgQEYGRkpNptZDmOwxcvXqC/vz+6uLjIraV169b47bff4pMnT9SujmJisRj/+usv/Prrr2VmcT4fBgYGOHr0aLxy5QqKRCLWkeXKy8vDPXv2YOvWrUutxcHBAQMCAjAnJ4d1VIUkJibi7NmzUUdHp8R2eOrUqRgfH886Ypk+ffqEq1evlrksODgYmzRpIlOLjY0N3rx5k1FK5UgkEmzXrh3q6Ohgenp6iSZk4sSJKnkxW+MakVatWml00yGRSDAsLAz37duH06ZNw9atWyu0o9bS0kIXFxf85ptv8PDhw/j27Vu12TkkJCTgsWPHcObMmejg4KBQLW5ubujr64sXL15Uu2l/eYdbSqvF3d0dv//+ewwODlbLHZ1IJMJbt27hvHnzsFGjRnJr6datG27evBmjoqJYxy4Tx3H4/Plz9PX1RWtr61Jr4fF42KtXLzx06JBSh3NZiY2NxaVLl8ocfvm8loEDB+Jff/2FEomEdVQZEokEDxw4UOLyzMxM9PPzQ0NDwxL1DB8+XO0PkYnFYuzTpw96eHggIqJQKEQ/P78Ss1Pjx49XmxeAivjjjz+k2du0aVMtTQhiDWxENKnpQERMT0/HK1eu4MqVK7F3795oYmKiUBNlZWWFPj4+uH79erx7967avALiOA6jo6PxwIEDOGnSpBKvDkoburq66OHhgX5+fnj9+nW12zEoe7ilcePGOHPmTDx79ixmZGSwjl+q7OxsPH36NI4fP17uLI6hoSEOGTIEDx48iKmpqczyCoXCcpeJjY3Fn376CR0dHcusx8XFBTdt2oQfPnyohtSKefPmDZ4+fbrE5RzH4Z07d8o8/GJiYoILFy7EyMhIBqnLJ5FIcPr06di2bVvpZXl5ebh+/fpS17nevXvjkydPGCZW3LJly6Tb4dDQ0BKzh2ZmZqU+pupMKBRi06ZNS33eqLIJQayhjYi6Nh1FRUX4/Plz3LFjB06YMAGbN2+uUNOhq6uLHTt2xAULFuAff/yBMTExajPbwXEchoeH486dO3HMmDHYoEGDcusxNDTEHj164KpVq/D27duYn59fLVkV2ZkVU/Zwy5AhQ5gebnn58iWmpaXJXSYpKQl3796N/fv3L3EC8OfDwsICJ0+ejBcuXFCL501oaCgOHTq01OsyMzNx79696OnpWWY9NjY2uGzZMpkT8NTF33//jaamphgQECC9rPjwi5OTU6n1tGjRAgMCAjA7O5thcvkkEglOmTIFAf6dpRaJRLhz585ST6Lv0KGDRp1ce/LkSZn8+vr6Mj/37dtXY84H+dz27dtLXd9atmyp8lnpGteI3LhxQyUbz+zsbHz79q1St0lKSsLz58/jsmXL0NPTE42MjBRqPGxtbXHkyJH4yy+/4IMHD7CgoKDK6/nSrVu38P79++UuJxaL8cWLF7hlyxb86quvsG7duuXWY2xsjP369cN169bh/fv3lWoIqkJKSgqOGzcOHzx4UOYymnq4paioCNesWYOGhoZYWFhY4vqIiAhcv349uru7yz3E17RpU1y8eDEGBgaqzQnNHMfhnj170MDAAHv16iW9vLCwEM+fP4/Dhg0rs6EyMTHBqVOn4p07d9TucEWxgIAA6eza0aNHyz38MmDAALU8/PIlsViMEydOlGbn8/mlvtJu2bIlnjt3Tm1eVCni1atXZW7HjYyMcOfOnRpVT7Hs7Gy0tLSU+2J4wIAB+OLFC5Xcf41rRKp6Wr+oqAh37dqFlpaWGBwcXOZyhYWFGBISglu2bMHRo0fLPdb+5exA165dccmSJXj27NlqnzKOjY3F4cOHIwDgu3fvSlwvEokwJCQEN27ciAMGDEA+n19uTWZmZujj44O//PILPn36lNlbVCUSCe7ZswdNTU1RW1tbpkGt6OGWM2fOqM3hlrCwMOnbT4vf0iyRSPD+/fu4dOlSbNGihdya2rdvj2vWrMHQ0FC123gKBAIcNWqUNOuUKVMwODgYZ82aVeqOunhjOWTIEDx9+nS1zbJVRFFREc6ZM0cme6tWrTTy8MuXxGIxjh8/Xu5617BhQzx48KDaNLyK+vTpU5mHmmvXro2vXr1iHbHCVq1aJfcxa9myJV64cEFl2wlqRMrAcRxeuXJFerzZyMhI+kqe4ziMi4vDkydP4qJFi9Dd3V3uVPfno1mzZjh+/Hjcvn07Pn36lNmr6fz8fFy1ahUaGBggAGDdunWR4zgsKCjAe/fu4Y8//oi9evVSaBbH2toaR44ciQEBARgaGqoWr9jCwsLQw8NDmtHJyUnjDreURSwW4/r162XWOUdHR5w2bZr0cwvK2lH36dMHd+zYoVbnSHzpyZMnJTb48hrFzp07444dOzA9PZ119HJlZmZi7969y31OacLhly8VFRXhmDFjyqzJwsICt2zZUurMnboTi8Xo7e0t9zGztbXFw4cPq8X2TxnJyclYu3btUmtq0KAB7t+/X+UvJqkRKcWLFy+wV69eMg+Ig4MDbty4scwPCyurS+7Zsyd+++23eOnSJaYn+xXjOA7PnDlTYsbG2toau3XrVuJ4Z2mjUaNG+PXXX+O+ffvw3bt3arWTzs/PRz8/v1LfDiivJnU63CLPmzdv0N3dXaH1D+DfV9SjR4/GP/74A7OysljHl4vjOPz1119RV1e33Lrs7e1x9erVav3unS9FRkbKnaXSpMMvXxKJRDhixAi5j1mvXr0wOTmZddQK8fPzK3edNDMzwylTpmB4eDjruEr58i26AICmpqa4YcOGaptZpEbkMx8+fMBJkyYp9HbZ0oajoyNOmTIF9+zZg69evVK7qcewsDDs0aOH0nU1b94cp02bhr///jvGxsayLqNM169fV+hdOsWjcePGOGPGDLU63FIWsViMmzdvls5gyRsNGjTA2bNn419//VXt5+NUVHp6Og4ePFhuXXXq1MF58+bho0eP1Kr5VcTt27fLPKT0+fbj48ePrKMqTSQS4bBhwxR6ztWtWxcvX77MOrJSTp8+XWY9VlZWOGvWLLx586ZGfUpysaioKJkXbfr6+rh06dJq3x5SI4L/fhLeypUrS31Pu7yNYr9+/fCHH37Av/76S63fK56RkYHz589X+PNVnJyccM6cOXjy5Em1+/Cw0iQlJeHo0aPLrat27dpqe7hFnnfv3skcZiprNG3aFB8/fqwxdRULCgpCGxubcuszMTFR6IRqdbN79+4SM3RlDRsbG5WdEKgKQqEQfXx8ym0++vbtiytWrMCzZ89iTEwM69gKCw0NLfFBeDY2NrhgwQK1OrG7ooq3m1paWjhlyhRmHyD3n25EioqKcM+ePXKPq38+PD098dChQ2r1YWHyiMVi3LNnD1pYWChcnyYcZy8mkUhw165dCp1AC/DvISVNeludRCLBbdu2KdUg//DDD6xjK0wikeDatWsVbpABAGvVqqUxb/UsKirCBQsWyK3H3Nwc27Zti4MHD8Y5c+bg+vXr8eLFixqxfSksLMRBgwaVmCHo378/rly5Ei9cuIDx8fEaUUtpMjIypO/2adKkCS5ZskQjZ+PK8vTpUwQAHDx4MIaFhTHNosz+m4eoDv96r3TZ2dnA5/NBIBCAiYmJ3GUREa5fvw5LliyB169fK3wf1tbW8PTpU2jQoEFl46rcgwcPYP78+fDs2TOlbrdnzx6YPn26ilJVndDQUJg5cyY8fPhQqdu1adMGAgMDy11HWHv//j1MmTIF7t27J3M5j8cDLS0t0NbWlvn6+fc///wzTJo0iU1wBSUnJ8OkSZMgJCQETExMpMPY2Fjm59Kus7S0BDc3N9YlyCUQCGDmzJkQGhoKtra2YGtrCw0bNpR+b2trCzY2NmBkZMQ6aoUUFhbC/PnzITk5GVxdXaFdu3bg6uoK9evXZx2tSkgkEli2bBkYGhrCsGHDoE2bNsDj8VjHqlI//PAD9OrVCzw8PFhHUWr/XaMakZSUFEhPT4dPnz7Bp0+fpN+XdtmnT58gMzMTEBHat28PgYGBYGBgUE2VVUxGRgZkZ2dLR05OjkJfCwsL4cCBA+Dk5MS6BLlycnKgsLAQhEIhiEQi6dfPvy/ra9u2bcHd3Z11CXIVFhYCx3EyjYaWllaN2RgWFRWBjo5OjannSxKJBLS1tVnHUBmO40BLS4t1DJVBxBq7bgL8Wx8AqE2Nyuy/daopk8rxeDywtrYGa2trhW8jkUggMzMTPn36BIWFhWrfiJiZmYGZmRnrGCpjbGwMxsbGrGOojLqvX5Wlq6vLOoJK1eQmBABqdBMCoD47aFXR5PrUuhEp7vCys7NVdh96enpQr149ld8PIYQQ8l9RvD9V5KCLWjciOTk5AABga2vLOAkhhBBClJWTkwN8Pl/uMmp9jgjHcZCYmAjGxsYaPe1UVbKzs8HW1hYSEhLU/sRMTUZ/5+pBf+fqQX/n6kF/Z1mICDk5OVC/fv1yD/up9YyIlpYW2NjYsI6hdorfcUBUi/7O1YP+ztWD/s7Vg/7O/6e8mZBiNfvsJEIIIYSoNWpECCGEEMIMNSIaRF9fH/z9/UFfX591lBqN/s7Vg/7O1YP+ztWD/s4Vp9YnqxJCCCGkZqMZEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBHRcEKhEFxcXIDH48E///zDOk6NEhsbC1OnTgU7OzswNDSEpk2bgr+/P4hEItbRaoSAgABo3LgxGBgYQMeOHeHx48esI9Uo69atg/bt24OxsTFYWlqCj48PvH37lnWsGm/9+vXA4/Fg4cKFrKNoDGpENNzSpUuhfv36rGPUSG/evAGO42D37t3w+vVr+PXXX2HXrl2wYsUK1tE03smTJ8HX1xf8/f3h+fPn0KZNG/D29obU1FTW0WqMe/fuwZw5cyAkJARu3LgBRUVF0KdPH8jLy2MdrcZ68uQJ7N69G5ydnVlH0SxINNbVq1fRwcEBX79+jQCAL168YB2pxtu4cSPa2dmxjqHxOnTogHPmzJH+LJFIsH79+rhu3TqGqWq21NRUBAC8d+8e6yg1Uk5ODtrb2+ONGzfQ09MTFyxYwDqSxqAZEQ2VkpIC06dPh99//x2MjIxYx/nPEAgEYGZmxjqGRhOJRPDs2TPo1auX9DItLS3o1asXPHz4kGGymk0gEAAA0PqrInPmzIEBAwbIrNdEMWr9T+9I6RARJk2aBLNmzQI3NzeIjY1lHek/ISoqCn777TfYtGkT6ygaLT09HSQSCVhZWclcbmVlBW/evGGUqmbjOA4WLlwIHh4e0Lp1a9ZxapwTJ07A8+fP4cmTJ6yjaCSaEVEjy5cvBx6PJ3e8efMGfvvtN8jJyQE/Pz/WkTWSon/nz338+BH69u0LI0aMgOnTpzNKTkjFzJkzB8LCwuDEiROso9Q4CQkJsGDBAjh27BgYGBiwjqOR6CPe1UhaWhp8+vRJ7jJNmjSBkSNHwqVLl4DH40kvl0gkoK2tDePGjYPDhw+rOqpGU/TvrKenBwAAiYmJ4OXlBe7u7nDo0CHQ0qL+vTJEIhEYGRnBmTNnwMfHR3r5xIkTISsrCy5evMguXA00d+5cuHjxIgQGBoKdnR3rODXOhQsXYOjQoaCtrS29TCKRAI/HAy0tLRAKhTLXkZKoEdFA8fHxkJ2dLf05MTERvL294cyZM9CxY0ewsbFhmK5m+fjxI3Tv3h1cXV3h6NGjtEGpIh07doQOHTrAb7/9BgD/Hjpo2LAhzJ07F5YvX844Xc2AiDBv3jw4f/483L17F+zt7VlHqpFycnIgLi5O5rLJkyeDg4MDLFu2jA6FKYDOEdFADRs2lPm5du3aAADQtGlTakKq0MePH8HLywsaNWoEmzZtgrS0NOl11tbWDJNpPl9fX5g4cSK4ublBhw4dYMuWLZCXlweTJ09mHa3GmDNnDhw/fhwuXrwIxsbGkJycDAAAfD4fDA0NGaerOYyNjUs0G7Vq1QJzc3NqQhREjQghZbhx4wZERUVBVFRUiQaPJhIrZ9SoUZCWlgbff/89JCcng4uLC1y/fr3ECayk4nbu3AkAAF5eXjKXHzx4ECZNmlT9gQgpAx2aIYQQQggzdNYdIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDPUiBBCCCGEGWpECCGEEMIMNSKEEEIIYYYaEUIIIYQwQ40IIYQQQpihRoQQQgghzFAjQgghhBBmqBEhhBBCCDP/D1eFOAr6tpGXAAAAAElFTkSuQmCC", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-5, 5, 10)\n", + "X, Y = np.meshgrid(x, x)\n", + "\n", + "# a)\n", + "u = 2*X + 3*Y\n", + "v = 1*Y\n", + "\n", + "plt.quiver(X, Y, u, v)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "524b01b5-ae1b-40e0-a11e-45faaf5bfaf1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "<matplotlib.quiver.Quiver at 0x7f9c04062810>" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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F5HI51q1bpzqDoXHjxhaz90AXpVKJEydOoG3btqp5Ma6urnj79q3oaOn26dMnHDp0CL169dJYwVjKLuS0lEolbt26hWXLlqFNmzZwcXHRWKG0aNHCYvb4REVF4cKFC1i6dCm6d++OUqVK6ZyT5e7ubvafvAp8fs2NHTsW9evX13m1zC+XqVOnWsT64/bt2/D29jaqJiJChQoV8Pr1a9GxjfLixQut173RtTdrw4YNFvGcAZ8bLF9fX6Nqa9q0aaYdljdl/JYBAJmp2NhYcnV1pZiYGHJxcREdR0NCQgKtWLGCFi9eTAcOHKDmzZuLjpQpXr9+TRs2bKDNmzdTtWrVyN/fn2QymehYGSKXy+ncuXN08OBBOnz4MMXHx9Ply5epevXqoqOlm0KhoNu3b9OFCxfowoULdPnyZUpISKCePXvS9u3bycrKSnREk8XGxtKdO3fo5s2bdOvWLbp58yY9efKEAJCbmxudOXOGqlWrJjqm0aKjoykwMJCePn2qWgIDAykwMJCSkpJUP/fDDz/Qhg0byMbGRmBa/T58+ECvX7+m4OBg1RIUFKT6f0hICCmVSrXfyZ8/Px0+fJhq164tKLVhSqWSZs6cSffv36fIyEiKiIigiIgIio6O1vt7/fr1ozVr1lCuXLmyJ2g6PH78mJo0aUKhoaFG/46npyft2LGDmjZtmqHHNmX85kYkE0RGRpK/vz/17t1bdJRMlZSURAcOHKCyZctSlSpVRMfJNAqFgv766y+6du0ajRs3juzt7UVHyhQpKSkUEBBAFy5coAoVKlCbNm1ER8oU8fHxdPfuXbp58ya9fPmSJk+eTJ6enqJjZYgkSRQcHKzWoJQqVYpGjBhhsU2/QqGg0NBQtUYlODiYwsPDadKkSVSxYkXREU2SkpKi1phoW3x9fWnevHnk6OgoOq5WACg5OZliY2ONWuLi4ig2Npbi4+Np+PDh1K5du3Q/NjcijDHGGBPGlPHb8vbdMsYYYyzH4EaEMcYYY8JwI8IYY4wxYbgRYYwxxpgw3IgwxhhjTBhuRBhjjDEmDDcijDHGGBOGGxHGGGOMCZNtjciiRYtIJpPRmDFjsushGWOMMWbmsqURuXHjBm3YsIEqVKiQHQ/HGGOMMQuR5Y1IfHw89ezZkzZt2kR58uTJ6odjjDHGmAXJ8kZk+PDh1Lp1a6M+yU/bh/MwxhhjLOfK0s+c3rNnD926dYtu3Lhh1M8vXLiQZs+enZWRGGOMMWZGsmyPSHBwMI0ePZp27txJDg4ORv3O5MmTKSYmRrUEBwdnVTzGGGOMmYEsa0Ru3rxJ4eHhVKVKFbKxsSEbGxu6dOkS/frrr2RjY0NKpVLjd+zt7cnFxUVtyUoAsvT+s0tMTEyOqCUoKIjkcrnoGBn25MkTioqKEh0jw+7fv0+vX78WHSPD7t27Z/ReWXP26NEj8vf317rutCTPnj2jnTt30qdPn0RHyZC3b9/SunXr6P3796KjZMjHjx9pyZIl9PTpU3EhkEViY2Nx//59taVatWro1asX7t+/b9R9xMTEgIgQExOT6fmePXuGmjVr4ty5c5l+39np3bt3KFmyJMaPHw9JkkTHSbeoqCgUK1YMX3/9Nd69eyc6TrolJSWhTJky8PT0xL59+yz2OZEkCdWrV4ednR1Gjx6N8PBw0ZHSrWXLliAiNG7cGKdPn7bY56RPnz4gIhQpUgSLFi2y2Odk/PjxICI4OTmhX79+uHjxIpRKpehYJlu6dCmICFZWVmjYsCHWrl2LsLAw0bFMtmPHDhARiAglS5bEjz/+iEuXLiElJSVD92vK+J1ljYg2DRo0wOjRo43++axqRM6cOYPcuXODiFCoUCFERkaqvmdJK6nw8HCULFlS9SKy1GZEqVTi22+/VdXh6emJixcvio6VLrNmzVLVQURo27YtgoKCRMcy2f79+9XqcHZ2xty5cxEfHy86mknu3r2rVgcRoXLlyti7dy8UCoXoeEaLjIyEg4ODWh12dnbo2bMn/vnnH4t53ysUChQoUEDjOfHz88O0adMQGBgoOqLRatasqVGHJTYlXbp00aiDiODu7o7vv/8e+/fvR2xsrMn3y42IAeHh4fDy8lL9wTt06KB6I2/ZsgWvXr3K1MfLKikpKRovIm3NiLmvpCRJwsqVK2FjY6Oqw9raGkuWLDH77F/y9/eHj4+P2nPi5OSEVatWWdTAd/PmTTRo0EBj5eTl5YV169ZBLpeLjmiUV69eoV+/frC1tdWopVixYli/fj0SExNFxzQoMjISkydPRr58+bQOGhUqVMD69esRFxcnOqpeiYmJWLp0Kb766iutdRARateujXXr1uHjx4+i4+okSRI2bdqEpk2bwtraWmsdltKU/Pnnn+jWrRtcXFx0Pid2dnb45ptvsGbNGqM3rMy2ETFVVh6aOX36tNofetOmTUhMTISvry8WL16c6Y+XVQw1I58+fcKyZcsEpzTO33//jYIFC6rV0qFDB63Pvzk3KHFxcRg9ejRkMplaLbVq1TL6sKQ5kCQJ/v7+qFChgsaKqUSJEhZ16Ck4OBjjxo1T7QlNu3h6emLhwoWIjo4WHdOgpKQk7Nq1C/Xq1dM6YDg7O2PYsGFm/zqTJAm3b9/GmDFjkD9/fp2DX6dOnfC///3PrBvfiIgIbNy40eKbkuTkZJw9exajRo1C4cKFdTYlqXsVZ8yYgYCAAJ3rAG5EjDRu3DjVH9bR0REjRowAEaFKlSpZ8nhZRV8zcvDgQTg5OeH9+/eiYxolLCxMY0u8ZMmSePDggepnJEnCvHnzBKY0zrVr1zS2/GxtbTFt2jStW+HmepxcqVTijz/+gJ+fn8YKqXr16jh//rzoiEb78OED5s6dq3XPgrOzMyZMmICQkBDRMY1y7949DBs2DE5OTloHi3r16mH37t1ITk4WHVUvuVyOY8eOoUuXLrC3t9daS758+TB69GjcvHnTrJvfnNKUSJKEe/fuYd68eahRo4bepqRQoUIYMmQI/P391dZr3IgYKSkpCRUrVtT6x7WkY5WA7makW7duICKMHDlSdESjpaSkqCa0pW0Ud+/eDQB4+fIliAinTp0SnNQwuVyOBQsWaKxgS5YsqTEPZvPmzfj3338FJTUsKSkJy5cvR968eTXeLy1atMCdO3e0/p457mJPSEjA6tWrtW752dnZYeDAgRazDoiNjcW6det0Hu7Inz8/pkyZgtevX4uOatDHjx+xYcMG1KlTR+fAV65cOfz8889mP6k9pzQlABASEoKNGzeiTZs2GnOV0i65c+dGhw4dsHXrVrx48YIbEUMSExNx7949zJ49W+sfdO7cuZn+mFlNWzOSenjA1tYWL168EB3RJAcOHICzs7NaPaNGjcKuXbtA9Hm+QkREhOiYRgkMDESjRo00XmcDBw5EVFQUAGDKlCnw8PDA8+fPxYY1IDo6GlOnTkWuXLk0Xmu9evXSmGM1atQo/Pnnn2LCGpCSkoKdO3dqPfwkk8nQqVMn3LhxQ+vvXrhwAUlJSdmcWDdJkvD333+jZ8+esLOz0zrotWnTBv7+/nr3vmX0bInM8uzZM8yYMUPnYQIrKys0b94cO3fuREJCgui4euWkpiQhIQFHjhxB//79dR5WSzv2cCOi5361DQppl/Lly2fqY2YXbc1I6tKjRw/R8Uz25MkTlC1bVq2OtAPgd999Z9a7atOSJAm///478uTJo1aPl5cX9u/frzo9s2TJkvjw4YPouAaFhIRgyJAhGitWOzs7jBkzRtUk9uvXDzY2NmbbjAD/Nx9G2wRdIkKTJk1w5swZtdfalClT0LBhQ1UjaU7Cw8OxaNEinYN4kSJFsHjxYq2N/L59+7B8+XKzeV8plUpcunQJ/fv319gwSV2cnZ0NngocHR1tFmfjZUVTIuo1qFQqceXKFUyePBnlypXTWgs3InrI5XL89NNPepuRtPMSLIFcLsepU6dUA5q25datW6JjmiwuLk51iEnbsmHDBtERTRIWFqa1nrRbsfXq1TOrrW19njx5gk6dOmkdHObOnYvvvvsORGT2zUiqK1euoF27dlpfa1WqVFGd+pu6N7V8+fIIDg4WHVsrhUKB48ePo3Xr1hqTp1Nfc7169VI7BfjUqVMgIvTp08fszihKSEjArl270KJFC1hZWWl9jnSdCpySkgI7OzvMmzfPbOZjZVZT0qtXL2zYsEF48/j8+XMsX74cjRo1Uj0/3IgY4eDBgzq77OnTp2fZ42Y2pVKJKVOm6Hwxpy7NmzcXHTVdFAoF2rZtq7WmXLly4fHjx6IjmuzYsWPw9fXV+Vz16NFD+IrFFFevXtW5RyF1sZRmBAAePXqk89Tf4sWLo3Hjxqqvvb29zX7D5dWrV0adAnzx4kXVbTVq1DDbuRghISFYsmQJypcvr/P19uWpwN7e3qr1oLldEC4jTcmECRNA9Pm6ReZyYsLr16+5ETHFkydPtO5WKlmypEUNBMDnWjp27Kh3MDh79qzomEaTy+XYtm0bypQpo7emKlWqmP3ZAdrExcWhdevWOuuypGYY+L9DHPquE2FJzQig/9TftIubmxv++usv0XENSj0FuG7dulrr+HJ+SYECBXDlyhXRsXUy5VTgQoUKqW4rWLAgLl26JDq+VqY2JfPmzVPdnj9/fhw7dkx0CXzWTHrEx8ejR48eGk+2JR7KAD7vXq5fv77WF3DVqlXNZtekIcnJydi/fz+++eYbrbuW0y4TJ04UHdckHz9+xLBhw3TuYk5dtmzZIjqqyRQKBaZPn55jmhFA/6m/qYu9vT32798vOqrR7t27h6FDh+o8BTjtQP7777+LjmuQMacCfzmYL1iwwKzXh8Y0JdqWoUOHCp3Ey41IOkmShNWrV6vtirW0wS0tSZJw/PhxrVune/fuFR3PZG/evMHs2bO1Xs+C6PMsbUu5pkXqQK2rli8HbUv6TCRJkrB+/Xo4OjoarMvSmhEAuH//vt69IzKZDL/++qvomCZJPQXY0J7H0aNHm81ZNYYYcypw6tKiRQuzO1SjjalNSalSpRAQECAkKzciGXTlyhXVscTChQtb3OGZLykUCmzbtk1tPkKxYsXM+mqF+iiVSpw+fRpdu3bV2I1cqFAhizjjJJUkSXj8+DGWL1+O5s2b69yKc3V1xcOHD0XHNYq/vz9q166t93oDltqM+Pv7w83Nzagt0okTJ5r1lvaXXr58idKlSxusq3Hjxmqfz2UJ/v77b62nNH+57rh8+bLoqEZLbUqqV69u8D22YMGCbP+ICW5EMkF4eDiaNm0KIsLVq1ez/fGzQmJiIpYtWwZ3d3cQEdasWSM6UoZFRkZi5cqVant9OnXqZLHNY0JCAvz9/TFy5EiUKFFCbYVSuHBhs76+wJdSUlJw584dbN68GYMHD0aVKlXUPk/I0pqR2NhYzJo1C927d0fVqlX1fjZH6tKrVy+LmLt0/fp1vdeE+HIpUqQI7t27Jzq2Ud68eaPxXtK1WFtbY+HChRbTQL59+xbFixc3qra6detm6+eomTJ+ywCAzFRsbCy5urpSTEwMubi4ZPvjK5VKmjlzJiUlJdHSpUuz/fGzSkxMDP3888+0e/duunfvHjk5OYmOlGEAKCAggH777TfavXs3rVy5kvr27Ss6Voa9ePGCTp06RSdOnKDz589TuXLl6OLFi+To6Cg6WrokJSXRvXv3KCAggG7cuEEBAQH06NEjsrKyon379lH79u1FRzQaAAoPD6dnz55RYGAgPXv2TPX/58+fU2JiIhERNWvWjA4ePEjOzs6CE+sWEhJCb968odDQUAoJCdH6b2RkpNrv5M6dm7Zt20YdO3YUlNowuVxOI0aMoHv37lF0dDTFxMRQdHQ0JSUl6f29li1b0vbt28nDwyObkpru3bt31LBhQ3r+/LnRv+Ps7Exr1qyhXr16kUwmy8J0po3f3IgY4fbt21S5cmVhj59VQkJCKDo6msqWLSs6Sqb69OkTnTp1itq0aUO2trai42Sa5ORk+vvvv8nGxoYaNGggOk6miY+Pp9u3b9Pdu3epe/fulDdvXtGRMkySJHr37p2qMXF2dqYePXpk+co/K8nlcgoLC1M1JqlLjx49qEyZMqLjmSQpKUnVlKT+m7qkfu3k5ERjx44lBwcH0XG1CgsLo9DQUEpKSlItycnJal/ruu27776jFi1aZGk+bkQYY4wxJowp47dVNmVijDHGGNPAjQhjjDHGhOFGhDHGGGPCcCPCGGOMMWG4EWGMMcaYMNyIMMYYY0wYbkQYY4wxJgw3IowxxhgThhsRxhhjjAnDjQhjjDHGhOFGhDHGGGPCcCPCGGOMMWG4EWGMMcaYMNyIMMYYY0wYbkQYY4wxJgw3IowxxhgThhsRxhhjjAnDjQgzS8nJyaIjMMYYywbciOQggYGBdOPGDdExMsXKlSvpzp07omOkiyRJoiNkiqSkJAIgOkaGxcXFkUKhEB0jw2JiYigxMVF0jAyLjY2lqKgo0TEyLD4+nkJCQkTHyLDExER69uyZ0Pf6f7oRSUlJISKihw8fWuzgAYCOHz9OiYmJNGjQIDp16pToSOkCgGbNmkUHDx4kIqK9e/fS5MmTBadKn2HDhtGIESM0Bo0DBw4ISpQ+o0ePpkaNGlFAQIDoKBkyffp0KlmyJK1evZoSEhJEx0m3ZcuWUYECBWjYsGEUEBBgsU3i77//Tp6entS6dWvaunWrxTYlhw4dokKFClGVKlVo+vTpdPXqVVIqlaJjmezSpUtUsmRJ8vPzo379+tHOnTspNDQ0e0PAjMXExICIEBMTkyn3FxsbCwA4duwYypYtC19fX+zatQve3t6Zcv/Z7e3bt2jZsiWICDVr1gQRoVGjRqJjmUySJEybNg1EBGtra/z8888gIhARzp8/LzqeSQ4dOqTKXq5cOdy9excAoFQq4eTkhKNHjwpOaJwHDx7AyspKVUvPnj3x+vVrjZ+7cuUKkpOTBSQ0zsePH5E7d25VHXny5MHUqVMRFhYmOppJFAoFfHx8VHUQESpUqIAVK1YgMjJSdDyT1K5dW60OW1tbtGrVClu2bMHHjx9FxzNa165d1eogIuTLlw+9e/fG3r17ERUVJTqiUX788UeNOogIZcuWxahRo3DkyBFER0ebfL+mjN//qUZk06ZNKF26NJo0aaL2By9Tpkym3H92+/DhA9zd3dVqsbe3R2JiouhoJomPj0f58uW1vhmqV68OSZJERzTa0KFDNZ6PFStW4NWrVyAiuLm54cWLF6JjGrRlyxbY2dlp1DJx4kS1ldL06dPRrl07yOVygWl1+/vvv5E/f36N15W9vT0GDBiAR48eaf29gwcPmlVNb968QenSpbW+R+zs7NC5c2ecPHkSCoVC7/2Ifi8lJSWhfv36kMlkWmuxpKakR48ecHBw0FoHEcHGxgYNGzbEkiVL8OjRI+F/e10mTZqkMY58uVhbW6NWrVqYOnUqzp8/j6SkJIP3y42IDikpKShVqpTGH9nS9iJcv34dPj4+sLa21vqiuXDhguiIJgsPD9fZjOzfv190PKNJkoRt27bByclJrYa0r7vKlSvj06dPoqMa9PLlS3Tr1k3j+fDw8MDq1ashl8sxbtw4EBG6dOmClJQU0ZG1SkxMxMaNG7W+94kIbdu2xaVLl9QGih49euCbb77JtHVPZpAkCf/++y8GDBig8fpKXXx8fDB9+nSdze78+fMREBCQzck1vX37FitXrkTdunV1Dn62trZo2bKlUU3J8+fPheyZS0hIwNGjRzFkyBCNPVZfLkWLFsXIkSNx8uRJozcWs6t5USqVuHnzJn7++Wc0b94cuXLl0ltLrly50KxZMyxatAgBAQFaG2BuRPQ4cOCAxh+1e/fumXb/2eX8+fNwdnbW+iKZMWOG6HhGS0lJwenTpzFw4EDkzZtXaz0lSpQwq61TYzx//lx1uEzb0r9/f9ERjXb16lXUqVNHo4aSJUuq1dizZ0+DW+QiKZVKHDlyBPXq1dO5923fvn1ISUlB//79QUSoWLEi3r59Kzq6hvj4eGzZskXvQN64cWPs2LFDremdPn067OzssHHjRrPZQs+MpuTQoUOoXLmyzj1c2UGSJNy9excLFixAnTp11A5tfrk4Ojriu+++w8aNG/W+vmJiYvDDDz9k+96hpKQkXLx4EdOmTUPt2rV1bvSmLnny5EGHDh2wdu1aPH36FJIkcSOijyRJqFatmtofcezYsZl2/9np1q1bWnc716tXT3Q0owUHB+P777/Xuas2dVm3bp3oqCaTy+WYNGmSzpo2b94sOqLRJEnCwYMHUbx4cb3PU79+/aBUKkXHNejq1avo1KmT1sGiSJEiqFixouprb29v3Lt3T3RknZ4+fYpJkyahQIECWp8TV1dXDB06FAEBAVizZo3q9r59+yIhIUF0fDXpbUru378PIoKDgwNWr15tFk1WZGQkduzYge7du8PNzU3v+6ZSpUqYNm0arly5otHMFy5cGF5eXjh06JCYQvB5LP7f//6H0aNHo1y5cnprSX3P9OjRgxsRfc6ePav2R1u8eHGm3n92evbsGYoWLarxRjW3FYwhd+7cUU281bZ4eXkhPj5edEyjKZVK7N27FyVKlNBZk729PW7evCk6qkmSk5OxYsUKvceUBw8ebBYDgTGeP3+OESNGGNwV7eLigrNnz4qOq1dKSgqOHj2Kdu3awcbGRmsdX+51rFixIp4/fy46ulamNCVpGywiQsuWLREaGiq6BJWUlBT89ddfmDhxosGB3MPDQ23C67fffqv6XufOnc1ionVoaCh27tyJfv36wdfXV2893Ijo0bRpU9Ufatu2bZl+/9kpNDRUbQuOiHDmzBnRsdLl/PnzqF69utYX9Lx580THM9pvv/2mdW/Vl0vhwoXx4cMH0XFNolAoVGc56VpGjhxpMc0I8Hnrde7cuXqfMxsbG2zdulV0VKOEhYVh6dKlKFOmjMHXoKurK44cOSI6sl7GNCXaBvTDhw+Ljq7Vq1evsGbNGrRs2RL29vY6a7C2tkaePHnUbnN3d8cff/xhNu8vSZLw7NkzrFu3Dp06ddLYSOFGRI/r16+r/lCnTp3K9PvPbtHR0WjQoIGqpilTpoiOlG6SJGH//v0aexOcnZ0REREhOp7RUlJScPbsWQwcOFDvHoTWrVtbxOEMAHjx4oXOORZfLj/99JPZrCyNdenSJdja2uqta/bs2RZTlyRJuHLlit4JrqnL5MmTzXbCcVqmNiUDBgxAXFyc6Ng6pU54HTx4MLy9vY1utFq1aoWgoCDR8TWkTnydM2cONyLG6NSpE4hIda0HS5eYmIj27duDiFC7dm3RcTJMLpdj3bp18PT0VL35xowZIzpWusjlcvj7+6NPnz5wcXHRWKnMnTtXdESjPH78GOvXr0ffvn11nk6adpkyZYrFDNpbt27Vu3Wadunbt69FTaB+9+6dzrPS0i6NGzfG+/fvRcc12tu3bzF//nyDdRUvXhxXr14VHdegtBNev/76a70TXlM3ztatW2eWGzI8WdVIT548gbW1NcLDw7Pk/kVQKBQYOHAgbGxszHorwBTx8fGYN28enJ2dYWdnh1evXomOlCGJiYk4fPgwunfvrrrYlkwmw+nTp0VHM9nHjx9x8uRJzJo1Cy1atNA6KW/27NmiYxoUGRmJBQsWoH///mjUqBF8fX0NTqBu1qyZWZ3eq8vTp0/h5+dn9JZ2wYIF8c8//4iObZS4uDij94xYW1tj9uzZFrHXBwA+ffqk9Ww1bUuDBg3w7Nkz0ZHVmDJ+ywDzvU5wbGwsubq6UkxMDLm4uGTJYwwbNoxWr15NVlY552r3AGj69OlUt25datGiheg4mSYiIoIWLFhAcXFxtHnzZtFxMsWnT5/o+PHjtHfvXrp27Rr9888/5OvrKzpWukmSRIGBgXT16lXVcv/+fVqwYAFNnDhRdDyTJCcn0+vXr+nFixf04sULevnypdr/k5KSqEKFCnT8+HHy9vYWHVenK1euUGBgIEVGRtKHDx9U/6b9f2RkpNrn8djY2NCyZcto5MiRJJPJBKbXLSEhgVq1akV//fWXSb9Xq1Yt2rFjBxUrViyLkmVcSkoKdezYkY4ePWr07zg4ONDcuXNp7NixZG1tnYXpjGPK+P2fb0Sio6PJzc0tS+5btPDwcMqfP7/oGJkuKCiIChYsSDY2NqKjZKq4uDgKDg6msmXLio6SqeLj4ykgIIAqVaqUY95rkiRRaGgovXz5kpKTk6lJkyZmO2AbAwDFxcVpNCm1a9c26wEbAKWkpFBSUpLakpycrPc2W1tb6t69O9nZ2YkuQasrV67QsWPHSCaTkUwmIysrK7V/9f2/Zs2aVK9ePdElcCPCGGOMMXFMGb9zzvEIxhhjjFkcbkQYY4wxJgw3IowxxhgThhsRxhhjjAnDjQhjjDHGhOFGhDHGGGPCcCPCGGOMMWG4EWGMMcaYMNyIMMYYY0yYLG1EFi5cSNWrVydnZ2fKnz8/tWvXjp4+fZqVD8kYY4wxC5KljcilS5do+PDhdPXqVTpz5gylpKRQ8+bNKSEhISsfljHGGGMWIls/ayYiIoLy589Ply5dovr16xv8ef6sGcYYY8zymDJ+Z+vHl8bExBARkbu7u9bvJycnU3Jysurr2NjYbMnFGGOMMTGybbKqJEk0ZswYqlOnDpUvX17rzyxcuJBcXV1Vi4+PT3bFY4wxxpgA2XZoZujQoXTixAn6+++/ydvbW+vPaNsj4uPjw4dmGGOMMQtidodmRowYQceOHaO//vpLZxNCRGRvb0/29vbZEYkxxhhjZiBLGxEANHLkSDp06BBdvHiRihQpkpUPxxhjjDELk6WNyPDhw2nXrl105MgRcnZ2prCwMCIicnV1pVy5cmXlQzPGGGPMAmTpHBGZTKb19i1btlDfvn0N/j6fvssYY4xZHrOZI5KNlyhhjDHGmAXiz5phjDHGmDDciDDG9FqzZo3oCJnqxIkToiMwxtL4zzUiL168EB2B/QdER0fThw8fRMfIsKSkJBoxYgRt3bpVdJRMM2TIEJo9e3aOOnSckJBA58+fFx2DsXT5TzUicXFx1LJlS4qLiyOFQiE6TobI5XLREbJETqgrISGBDh8+TAsXLhQdJUNOnDhBp0+fJiKiAQMG0NGjRwUnSp9NmzbR6NGj6dmzZ0RE5OLiQrNmzaLu3btTYmKi4HTG27hxI3Xs2JH27NlD8fHxat9zdHSk9u3b008//aR2UUhztH37dmrQoAHNnz+fbty4QUqlUu/P//jjj/Tu3btsSme8Q4cOUaVKlWj48OG0e/duCgoKMun3nz17ZhbN8MWLF6lkyZLUvXt3Wrp0KV24cEH1cSzpka6aYMZiYmJARIiJicmU+5s5cyaICCVKlEC3bt2QkpKSKfcrwuHDh7Fo0SIMHDgQgYGBouNk2M6dOzF79mx06tRJdJQMefDgAQoWLIgiRYrAzs4Or1+/Fh0pXaKiopA/f34QkWpxcHDA33//LTqaSZRKJYoVK6aqoVWrVvDz81N9Xb16dbx79050TKPUrVtX7bno0KED9uzZg7i4OABApUqVQESoUKEC7t+/Lzitbl26dFF7Xbm7u6Nz587YtGkT3rx5o/Hz7du3h7OzM3799VcoFAoBibUbM2aMWh1EBG9vb3Tt2hW//vorbt68qXeM+eWXX1C7dm1cu3YtG1Nr+vnnnzXqSDtOLlmyBOfPn0d0dLRR9xccHIzvv/8ed+/eNXr8/s80ImFhYcidO7fqj+zh4YHQ0NBMSCnG7t27VbXUqVMH27dvFx0pXZKTk/H999/D29sbRIQ8efKIjpQhq1atUnsz9+nTR3SkdNmwYYPWlZObm5tZD3JfOnfunNY60i6FChXCzZs3RUfV6/3795DJZFrzpzYlZcuWVd1mb2+P5cuXQ6lUio6uRpIk5MuXT+/zUapUKYwYMQL/+9//EBsbi3nz5qm+V61aNdy6dUt0GQCA2rVrG3xtOTk5oUmTJpgxYwZOnTqlNpYFBASofu77779HcHCwkDp69OhhsA5Tm5NSpUrBxsaGG5EvDR8+XOOPWrRoUQQEBGRC0uy3ZcsWVR2VKlVCUlKS6Ejpdv78edVKNleuXKLjpIskSZg+fTrs7e3VXmMymQz37t0THc9kr169QsmSJbWujAoWLGgxe3okScLFixfRoUMHWFlZ6VzB5sqVCwcOHBAdV68XL15g0aJFqFq1qtEDR7Nmzcxuj09kZCT27duHAQMGwNfXV29+GxsbFC5cWO02KysrjB07VrUnSJSEhARcvHgR8+fPR6tWreDm5mbw+bCyskLFihUxfPhw/PHHH7C1tVV9z9HREbNmzUJCQkK21iGXy3Hnzh1s3rwZQ4cORY0aNTTWY6Y2JyNHjlR9nxuR/+/58+eq7ix1ad++PR49epRJSbPf+vXrVVtDDx8+FB0nw8aPH696o0qSJDpOuigUCmzbtk1j5dqmTRvR0Uyydu1aODo66l35lCxZEuHh4aKjmuTAgQMGV6rz5s2ziNefKU2Ju7u72TZZkiThyZMnWLVqFdq2bQsnJyejB0AfHx8cPnxYdAkqSqUSDx48wIYNG9C7d2+1Q4KmLN7e3tixY4fQvVkZbU5cXV25EflSt27dVH+UunXr4t9//82khOKsWLECRIRVq1aJjpIpkpKSULFiRRAR5HK56DgZkpiYiGXLlsHd3V31urt06ZLoWEZLTEzExYsXMXPmTNSvXx92dnZaVzbVq1cXvlVqrP3798PBwcGolWjPnj2RmJgoOrLRAgMDVYc29S19+/bNtPl2WSU5ORmXLl3CtGnTUKNGDZ2Ho9Iu7dq1Q1BQkOjoWoWGhuLAgQMYO3YsatSoobFBrG+pWbMmrly5IroElfQ2J9yI4P+Ow5UrVw5Hjx61iK0dYyxatAgtWrTIMfUAnyd62tvbIzY2VnSUTBEdHY0pU6YgV65cqFWrlsU+VwkJCTh79iymTp2Kr7/+Wm1l2qxZMyQnJ4uOqNfbt28xcOBANG/eHGXKlFGbK6ZrqVWrFsLCwkRHN0ihUJh0jL9IkSIWNeF40aJFRtXl5OSEFStWmNVkVm3SHs4xdFgqdenRo4fZNlrGNCfciAD44YcfsHXrVrN/gZpqzZo1CAkJER0j061cudLidvkb8u7dOwwaNAj/+9//REfJFHFxcThx4gQmTJiA6tWro1evXmY3KVIfSZLw8eNH3L17F8eOHcO6deswZcoU9OrVCw0aNEDRokVhZ2cHHx8f3LlzR3RcvZYtW4ayZcuiWLFiKFSoEPLmzYvcuXPr3fK2srLCtGnTzH7P46FDh/TO69G2VKlSxSLm/V28eNGkvSO5cuXCjBkzEB8fLzq6QQcPHjS5EcnSD73LqIx+6J1CoSCFQkEODg5ZkE4suVxOdnZ2omNkOkmSSKlUkq2tregomS4+Pp6cnJxEx8h0MTExZG1tnaNqkySJIiIiKCoqikqXLi06TrooFApKTk6mpKQk1b9p/+/n50cFCxYUHVOrmJgYmjRpEimVSrKzsyN7e3u9/6b9v6OjIzVo0IBsbLL0o9TS7dWrV1S9enXVBQ+trKzIzc2N8uTJo/Pf1P+XLVuWKlSoILgC3Z4/f07VqlVTuw6JMeN3jm5EGGOMMXPy8uVLiouLUzUZTk5OZGVl+dcWBUDz58+n9+/fk5eXF7m6utLIkSO5EWGMMcZY9jNl/Lb8NowxxhhjFosbEcYYY4wJw40IY4wxxoThRoQxxhhjwnAjwhhjjDFhuBFhjDHGmDDciDDGGGNMGG5EGGOMMSYMNyKMMcYYE4YbEcYYY4wJw40IY4wxxoThRoQxxhhjwnAjwhhjjDFhuBFhjDHGmDDciDDGGGNMGG5EGGOMMSYMNyKMMcYYE4YbEcYYY4wJw40IY4wxxoThRoQxxhhjwnAjwhhjjDFhuBFhjDHGmDDciDDGGGNMmP9UIwKA7ty5IzoGY4z9592+fZsAiI6R6XJiTVntP9GIKBQK2rdvH1WvXp3WrFkjOk6mAEBnz54lSZJER2GMZQOlUknnzp3LMQPd6tWrqUaNGrR//35SKpWi42SaM2fO0PDhw+nx48eio2QqALRq1Sp69epVpt93jm5EEhMTad26dVSqVCnq2rUr3bx5k7p06SI6VoZdvXqVGjVqRDNnziQrK8t/CpVKJSUnJ4uOwXKo5OTkHNGwW1tb09SpU6lJkyZ07do10XEyrHPnzhQQEEBdunShUqVK0fr16ykxMVF0rAxr0KAB7d69m8qWLUtNmzalI0eO5IhGSyaTUUhICBUrVoxatGhBhw4dopSUlEy5b8sfxbT4+PEjzZs3j/z8/GjYsGH08uVLIiKytbWlFy9e0KRJk+h///uf4JSme/jwIbVv355q165Nly5dovLly9PTp09Fx8qQoKAgatKkCX369El0FJZDxcfHU9OmTSk4OFh0lAx5+vQpffXVV3ThwgWqVasWdejQwSK3ug8fPkyTJk2i169fk42NDRERvXjxgoYOHUqFCxem+fPnU1RUlOCUhp06dYpGjRpFP//8M+3atYsuX75Mr169IplMRt27dycionPnzlG7du2oePHitGTJEvr48aPg1Jr++ecfGjRoEE2fPp3WrFlDBw4coMuXL1NgYCDFxsaq7YHr378/AaBTp05Rhw4dyM/Pj6ZNm0Zv3rzJWAiYsZiYGBARYmJijPr5N2/eYMyYMcidOzeISO8yaNCgLE6feV6/fo2+ffvCyspKo4527dqJjpduu3btgqurK2QyGQYOHCg6ToYlJCRg5cqVUCgUoqNkmEKhwIoVK/Dp0yfRUTJswIABkMlkcHNzw+7du0XHSbdvv/1W4/1vZWWFfv364c2bN6LjGa1///4G18+5c+fG2LFjERQUJDquTlOmTNGZ39HRUevtDg4O6N+/P+7cuSM6vsqqVav0PhcODg7w8/NDjRo18O2332odX2UyGVq2bInDhw8jJSUFgGnjd45oRO7du4devXrB2tra4As8dWncuHE2VZF+4eHhGDNmDOzs7HTW4efnJzqmyaKiotCjRw+1OqpWrWrxA/jChQthb2+PW7duiY6SYQEBAbCzs8PixYtFR8kQhUKBKlWqqL3WevbsiaioKNHRTObj46NzPWBnZ4exY8ciIiJCdEyDGjRoYPR62sbGBr1798b9+/dFx9bQu3dvo+vQttSrVw/79u2DXC4XWse0adMyVMeXS6FChTBjxgw8fPgw5zcikiTh4sWLaNmypclP/vz583H8+HEBFRknNjYWs2bNgpOTk95arK2tERAQIDquSS5cuKBaoTo4OMDNzQ1eXl4oX748AgMDRcdLt6ioKIwaNQqvX78WHSXTvHz5EiNHjrTIQTvV06dPUb58eXh5ecHNzQ0ODg4gIvj6+uLixYui45nk+vXrBje2nJ2dMWfOHMTFxYmOq9OxY8cwf/581K1b16R1d+vWrXHp0iVIkiS6BADA33//jVWrVmHChAno0aMH6tWrhyJFisDW1tbkgXvevHl4//69kDru3LmDTZs2Yd68eRgxYgQ6d+6M+vXro1SpUnB1dU13QyKTyYxuRGSA+U7Bjo2NJVdXV4qJiSEXFxe17ymVSnr8+DE9ffqUAgMD1f7VdxyuVKlSdOvWLXJ0dMzq+OkWFxdHQUFBFBYWRqGhoRQWFqa2pN728eNHKlu2LF27do2cnJxExzZKXFwc2dvbk62tLclkMtFxMg2AHFVPWjmtNgAkl8tJLpeTs7Oz6DhGiYuLoxo1atCTJ0/I3d2dChQoQF5eXmpL2tt8fX3NuraEhASqXLkyPXv2TOfPuLu7U6lSpahUqVJUsmRJ1b9lypQha2vrbExrmo8fP1KpUqUoMjJS58/IZDIqVqwYVaxYUbVUqVKFvL29szGpcZKSkig8PJzev39PZ86coalTpxr8nSJFilDFihXp8OHDWsfvL1lsI6JPZGSkRnPy9OlTev78Ocnlcho5ciT9+uuvWZg8eyQnJ1N4eDg5OzuTm5ub6DiMsSwSHR1NcXFxlD9/frK3txcdJ8OGDx9Oa9euJTs7OypRooSq0UjbdOTNm1d0zHTp378//f7776qvnZycqEKFCmpNR/ny5S1m4zGVJElUt25dunLlitrtPj4+VK1aNdVStWpVyps3r0njt01WBhfFw8ODPDw86Ouvv1a7XalU0ps3b+jZs2ckl8vJzs5OUMLMYW9vTz4+PqJjMMaymJubW47Z2EhOTqZvv/2WfvrpJ/L19TXrvRumevjwIUVFRdHMmTNVTUfhwoVzxGUWNm/eTK9evaK2bduqNR2enp4Zvu8cuUeEMcYYY5knOjrapGbYlPHb8ts0xhhjjGWprNwjx40IY4wxxoThRoQxxhhjwnAjwhhjjDFhuBFhjDHGmDDciDDGGGNMGG5EGGOMMSYMNyKMMcYYEybLG5E1a9ZQ4cKFycHBgWrWrEnXr1/P6odkjDHGmIXI0kZk7969NG7cOJo5cybdunWLKlasSN988w2Fh4dn5cMyxhhjzEJkaSPyyy+/0MCBA6lfv35UtmxZWr9+PTk6Oqp9IBBjjDHG/ruyrBGRy+V08+ZNatq06f89mJUVNW3aVOPT+1IlJydTbGys2sIYY4yxnCvLGpHIyEhSKpUan8zn6elJYWFhWn9n4cKF5Orqqlr4k2UZY4yxnM2szpqZPHkyxcTEqJbg4GDRkRhjjDGWhWyy6o49PDzI2tqa3r9/r3b7+/fvycvLS+vv2Nvbk729fVZFYowxxpiZybI9InZ2dlS1alU6d+6c6jZJkujcuXNUu3btrHpYxhhjjFmQLNsjQkQ0btw46tOnD1WrVo1q1KhBK1asoISEBOrXr19WPixjjDHGLESWNiJdu3aliIgImjFjBoWFhVGlSpXo5MmTGhNYGWOMMfbfJAMA0SF0iY2NJVdXV4qJiSEXFxfRcRhjjDFmBFPGb7M6a4Yxxhhj/y3ciDDGGGNMGG5EGGOMMSYMNyKMMcYYE4YbEcYYY4wJw40IY4wxxoTJUY0IAAoJCSEzPiOZMcYYY2lk6QXNslpoaCgFBASoLT169KDly5eLjpZhSqWSXrx4QXfv3lUt/fv3p3bt2omOlmlSUlLo1atX9PTpU6pevbrOzyBijDGWdfz9/SlfvnxUsmRJcnV1zfbHt5hGJCIigm7evKlqOG7cuEEhISFqP1OoUCGaM2eOoITpFxsbS/fu3VNrOh48eECfPn1S/UydOnXo22+/FZgyfQDQ+/fv6enTpxQYGEhPnz5V/f/ly5ekUCioSZMmdPr0adFRMyw+Pp7CwsLI3t6efHx8RMdhjGWRpKQkCgwMJC8vL/Lw8CArK8s+uBATE0OtW7cmIiJPT08qWbIklSpVSvVvqVKlqEiRImRnZ5clj28RV1b18fGh4OBggz/fq1cv6tWrF3l5eZGnpyfly5ePrK2tsyGp8d6/f0///POPWtPx+vVrvb9jZWVFV69eperVq2dPyHS6f/8+PXz4UNVwBAYGUmBgIMXGxur8HVdXV7p//75ZD9yJiYn06NEjCgsLo7CwMAoNDVX9P+2SkJBA7u7udOvWLfLz8xMd2ygfP34kpVJJDg4O5ODgQDY2NiSTyUTHyjBJkkgmk+WIWr6kVCrNbr2WXkqlkpKTkykpKYmSkpLIy8vLIgZ1ANSzZ0/avXs3WVtbU/78+alAgQLk5eWldSlatCgVKlRIdGy9unXrRnv37tX5fWtraypatKhGk1K9enXKnTu3xs+bdGV0mLGYmBgQUboXmUyG/Pnz46uvvkLTpk3Rq1cv/Pjjj/j555/h7+8vpKbk5GTs3LkTtWrVMrkeV1dXlCtXDt988w0GDBiAWbNmYdeuXULq0Ob169cYNWoUHB0dja6paNGiGDt2LNauXQuFQiG6BK2USiX27t2L4sWLG6xnw4YNkCRJdGSjvXnzBg0bNlR7z+TKlQseHh44deqU6HjpJkkSRo0ahQsXLoiOkmnCwsIwcuRIPHr0SHSUdIuOjkbdunXh5OQEGxsb1evO3d0d+/fvFx3PJKGhocifP7/e9YG9vT1+/PFHREZGio6r06VLlzBr1iy0adPGpPGoYcOG8Pf317m+Sx2/Y2JiDGawiEZkzZo1qFmzZoaaki+XNm3aiC4PN27cQJ8+fWBnZ5fuOipWrCi6DA2RkZGYPXs2PDw8jK7Dzc3N7AdwuVyO9evXo0CBAnpriYiIEB3VJEqlEj///DNsbW1VNXh6eiIoKEh0tAy5ePEiiAi//fab6CgZFh4eDk9PT/Tq1Ut0lAzr27ev2vuladOmePv2rehYJmvfvr3OdYCVlRX69+9vEe+hn376yaSN+44dO+LatWsG7zfHNSKphdy5cwdDhw6Fs7Oz1j9St27d0KJFC1SuXBkFChSAtbW1zj9o//79BVf3f8LDwzF//nx4e3trzers7AwnJyet32vdurXo+DolJCRgzZo1KFKkiMEXeLVq1UTHNVpCQgIWLVoENzc3jTr8/PxEx0u327dvo2zZsiAiNG7cGCkpKaIjZdjvv/+O+Ph40TEyxbFjx/Dy5UvRMTJsxYoVyJs3L+zt7bFixQoolUrRkdJl3rx5WtdlHTp0sKi9VuvXrze4fra3t8egQYMQGBho9P3m2EYkVVxcHDZt2oTq1aur/bF2796t9nNKpRIRERF48OABzp49i507d+KXX37BxIkTceDAgewsxSgpKSnYv38/6tevr1ZX9erVIUkSoqOjcf/+fZw4cQIbN27EjBkzsH37dtGxDUpJScGePXtQuXJljRf44sWLsWTJEmzatEl0TJN9/PgRkyZNQq5cuUBEaNCgAZ48eSI6VoZ8+vQJI0eOxJkzZ0RHYTlY27Ztce/ePdExMuT9+/dYtWqVal3WqFEjo/YUmJv79+9j2rRp2LZtG4oVK6a2fnZ1dcXkyZMRGhpq8v3m+EYkrZs3b2Lw4MFwcnJCkyZNsjFd1rpz5w4GDBigGuQsqcPWRZIknDlzBk2bNlW90OfMmSM6Voa9e/cOgwcPhouLC5KSkkTHyRTJycmiI7AcLKe8voYMGYIqVarg9OnTZn9o2ZC3b99CJpOBiFCoUCEsXboUsbGx6b4/UxoRizhrxphZt3FxcbR3717q3r271hm8lurjx4/0+++/k4uLCw0aNEh0nExz69YtWrJkCT158oRu374tOk6mePbsGbm6ulL+/PlFR2GMZYN///2XatWqZRFn+hjy66+/0oYNG2j8+PHUo0ePDJ+qa8r4nWMaEWaZXr58Sd7e3ll2fjpjjDHDAgMDqXjx4pnWVJkyflvMBc1YzlS0aFHRERhj7D+vZMmSwh7b8vcnMcYYY8xicSPCGGOMMWG4EWGMMcaYMNyIMMYYY0wYbkQYY4wxJgw3IowxxhgThhsRxhhjjAnDjQhjjDHGhOFGhDHGGGPCcCPCGGOMMWG4EWGMMcaYMNyIMMYYY0wYbkQYY4wxJgw3IowxxhgThhsRxhhjjAnDjQhjjDHGhOFGhDHGGGPCcCPCGGOMMWG4EWGMMcaYMNyIMMYYY0wYbkQYY4wxJgw3IowxxhgThhsRxhhjjAljIzqAMebPn09RUVFERLRq1Sqyt7cXnCjj5HI5RUVFUVRUFEVHR5ONjQ1Vq1ZNdCzGGGMsW1lEI/Lzzz+TtbU1nT9/3qybkFevXtHFixcpOjpa1WCkbTbS/puYmKj6PTs7O7pw4YLA5PoBoEuXLlFYWBjJ5XJKTk42+t+UlBRasGABlShRQnQZWsXGxtKVK1fIwcGBHBwcyN7eXvX/tF/b29uTlZVl7UAMDAwkpVJJPj4+5OTkJDpOplEqlfTmzRsqUqQIyWQy0XEyVXR0NLm6uua4uoiIkpKSyMHBQXSMTJdT61IoFJSUlJQ96w6YsZiYGBARiAgzZ84UHccgSZKwe/du+Pj4qHIbs2zZskV0dIPCwsLQo0cPk+oiIixbtkx0dIP27duHPHnyGKzFzs4Ozs7OyJcvH3x8fNC/f38oFArR8XWKjIxEw4YNQUTIkycPKlSogNatW2PIkCGYP38+tm/fjosXL+LFixdISkoSHdckv/76K3x8fNC7d29s2bIFr1+/Fh0pU7x8+RLffPMNrl27JjpKpvvpp58gSZLoGJkqMTER06ZNEx0jU0mShD///BMtWrTI0HohdfyOiYkx+LMW04gQEQoXLoyOHTtiwYIFOHXqFCIjI0VH1CohIQFz5syBo6OjwcHN0dERI0eOxJ49exAcHCw6ukGnT59GsWLFjGpCunbtajErnrdv36Jp06ZGN1j16tVDXFyc6NgGJScnY+DAgUbV5OnpiWrVqqF9+/YWMRBOnTpVLX+RIkXwww8/4I8//sDbt29Fx0u30aNHg4jQqVMnPH36VHScTFOsWDHs2LFDdIxMNWbMGHTt2lV0jExz6dIl1KpVC0SEP/74I0P3lWMbEW2LOTcnb9++Re/evU3ag+Dr64vu3btj9erVuH37tllucX/69AlTp06Fra2twXq8vb3xww8/YPfu3YiIiBAdXS+lUonly5fD3t5eb0329vY4fvy4WT432kiShOXLl8PKysrg8yWTybB8+XKLaCAlSdLbZJUoUQKDBg3C7t27ERoaKjqu0cLDw+Hs7AwigrW1NYYMGYKQkBDRsTKsXLlycHFxyTF7r06fPg0iQp8+fURHybD79++jTZs2qvdOxYoVoVQqM3SfOa4RcXV1NWrvgrbm5PTp0/jw4YPQOq5fv46vv/7apIYkdXF2dkazZs0wa9YsnD171qy2wh8+fIi6desaXYtMJkPVqlUxefJkXLhwAcnJyaJL0OrevXv46quvDNbj5eWFESNG4NKlSxbRlBw/flw1wOlapkyZYhFNSCqFQoH27dvrrcnGxgZTp05FSkqK6LhGmzNnjloNjo6OmDp1KqKjo0VHS7eqVauCiFC/fn2LeL/oExkZiYIFC4KIMHjwYNFx0u3Nmzfo06cPZDKZ2uvN398/w/ed4xqRatWqQaFQ4OHDh9i2bRtGjRqFOnXqpKs5WbhwoZDmRJIk7NmzB76+vmq51q5dizlz5uCbb76Bi4uLwTqsra1RpUoVszmco1QqsXnzZo05Fr6+vsibN6/eWnLnzo3WrVtjxYoVePTokVkNgImJiRg3bpzRry9LaUoePHiAIkWK6K2lcuXK+P3335GYmCg6rlESExPRoEEDnY38zZs3RUc0WVxcHDw9PdVqsbW1RZ8+ffDp0yfR8dKlTp06qloWLVokOk66SZKEjh07qmoZPXq06Ejp8u7dOzRq1EjjPdOwYcNMWRfnuEZEJpPh48ePGt/PSHNSpkwZARV9Pqwxb9485M6dG0SEDRs2qNVz9+5drF27Fj179kThwoUN1pE7d26z2NJ7//49vv/+e1Wu9u3bQ6lUIiAgAAsXLkSjRo0MHsoR3VRpc/bsWRQqVEiVMU+ePBg9erRqa0jbcubMGdGx9QoPD0e9evUMvraWLl0qOqrRoqOjUbFiRa11DBo0SHS8dFm7dq1aHf369RMdKUOaNGkCIoKTkxO6d+9uUYfL0rpy5Qo6dOigel4mTpwoOlK6yeVyVK5cWe11llnzw3JcIzJ16lScPXvWqN9RKBR48OCBweakV69eWZxev3fv3qFv374Gc7x79w779u3D6NGjUa1aNVhbW6vV0bhx42xKbJyzZ8+iRIkS8PX11fheXFwcjh8/jtGjR6NMmTJm0Rga48OHD+jcubNqj5RcLodSqcTff/+NUaNGqTUl7u7ukMvloiMblJSUhH79+qly29jYYMSIEXBycgIRwcHBwazmWxkjNDQURYsW1diL8PjxY9HR0kUul6N48eLw9PSEr6+v2Te4howaNQrr1q3DqlWrzGrvZ3pER0dj9uzZ2LBhg0U17NqsXLkS5cqVg0wmQ6dOnTLtfk1pRGQAQGYqNjaWXF1dKSYmhlxcXNJ9P0qlkp48eUI3b95ULb169aIhQ4ZkYtr0efPmDfn5+Rn98wkJCXT9+nX6559/6J9//qFGjRrRhAkTsjCh6ZKSkmjhwoU0duxYcnNz0/lzb9++pTNnztDp06epVKlSNGvWrGzLaCoAtGPHDho+fDjdvHlT7bookiTRlStXaN++feTk5ETz588XmNR4AGjZsmU0YcIEAkByuZw+ffpEW7dupejoaJo5c6boiCZ78eIFff311xQeHk6//fYbOTs7U+fOnUXHSrf9+/fT1atXacGCBWZ9DSVjKBQKsrGxiEtXmSQn1JWcnEytWrWidevWUcmSJTPlPk0Zv/8TjQhjmeX169ekVCqpWLFioqNkmqNHj1KPHj3o9evXlDdvXtFxMuz27dvUoEEDOn36NNWqVUt0nAwBQG/fviUfHx/RUVgOFxQURL6+vpl2f9yIMMZMcu/ePSpYsCB5eHiIjpIpLly4QEWLFjVpbyNjLPOYMn5b9v4kxlimqFChgugImapRo0aiIzDGjGRZH57BGGOMsRyFGxHGGGOMCcONCGOMMcaEyZJG5PXr19S/f38qUqQI5cqVi4oVK0YzZ84kuVyeFQ/HGGOMMQuVJZNVnzx5QpIk0YYNG6h48eL04MEDGjhwICUkJNDSpUuz4iEZY4wxZoGy7fTdJUuW0Lp16+jly5dG/w6fvssYY4xZHrM8fTcmJobc3d31/kxycjIlJyervo6Njc3qWIwxxhgTKFsmqz5//pxWrVpFgwcP1vtzCxcuJFdXV9XCVxNkjDHGcjaTGpFJkyaRTCbTuzx58kTtd969e0ctWrSgzp0708CBA/Xe/+TJkykmJka1BAcHm14RY4wxxiyGSXNEIiIi6MOHD3p/pmjRomRnZ0dERCEhIdSwYUOqVasWbd26laysTNsBw3NEGGOMMcuTZXNE8uXLR/ny5TPqZ9+9e0eNGjWiqlWr0pYtW0xuQhhjjDGW82XJZNV3795Rw4YNyc/Pj5YuXUoRERGq73l5eWXFQzLGGGPMAmVJI3LmzBl6/vw5PX/+nLy9vdW+Z8Yf9ssYY4yxbJYlx0v69u1LALQujDHGGGOpeOIGY4wxxoThRoQxxhhjwnAjwhhjjDFhuBFhjDHGmDDciDDGGGNMGG5EGGOMMSYMNyKMMcYYEyZLLmiWEz19+pT27NlDkiQRAI1/9d1Wp04d6tq1q+gStAJABw4coODgYHJwcFAt9vb2Wv//5de5cuUiGxvzfBlFRUXR3r17yc3NjfLmzUseHh6qfx0dHUXHy5CrV69SWFgYFStWjIoWLUq5c+cWHSlTKBQKOnHiBFWoUIF8fX1JJpOJjpRpXr58STKZjIoUKSI6SqZ7/PgxlSlTRnSMTBcREUGurq6qz0/LSSIjI8nDw0N0DCLiRsRopUqVoho1atDgwYNN+lTgKlWq0Ny5c7MwWcbIZDJq2bIljR07ljZv3mzS75YoUYIuXLhAhQoVyqJ0GZMnTx4qXbo0de3alcLDw9W+5+DgoNGcpP3Xx8eH2rdvb7YDYaVKlahfv360Z88eIiLy9PSkYsWKaSxFixal/Pnzm20dX7KxsaFcuXJRqVKlyN3dnWrVqqVaqlatatENV6FChahBgwYEgLp160adO3fWuPK0pTp//jz9+OOPtGjRIqpQoYLoOJkGALVr1472799v0a89bSZOnEibNm0yj8+BgxmLiYkBESEmJkZ0FJXY2FgMGzYMRGRw8fb2xvv370VHNtqhQ4eQN29eo2orUaIE3r59KzqyUd69e4c6deoYVRcRwc3NDX///bfo2AYplUpMnDjRYD1OTk6oUKEC2rdvj59++gmPHz8WHd0gf39/2NnZqdVhbW2NypUrY+jQodi2bRuePn0KSZJERzVJUFCQ2nusbt26WLVqFUJDQ0VHy5Dk5GQULVoUMpkM33//PV69eiU6UqYpX748atasicjISNFRMlWBAgWwa9euLLt/U8ZvbkTS6dKlSyhRooTBQaBw4cIYPnw4/P39kZiYKDq2QSEhIWjRooXBur7//ntcv37dYgYCuVyOMWPGGKzL09MT9+/fFx3XJOvWrYOVlZXB2mQyGebPn28xz9mRI0dgY2OjtyZ3d3e0bNkSs2fPxoULF0RHNsrp06chk8nU6rCyskLjxo2xYcMGix3wdu/erarHzs4OY8eORUREhOhYGTZy5EgQEUqXLo03b96IjpMpFAoFrK2tUbRoUSQnJ2fJY+S4RmTv3r2IjY0VHUfDp0+fMGHCBKMGASKCo6Mj2rZti/Xr1yM4OFh0fJ0kScLq1avh4OBgVKM1fvx4i2lK9u7dCycnJ72DdbNmzbBnzx6LaBxTHT16FI6Ojnqfq40bN4qOabIDBw7A2tra4OuwfPnyuHXrlui4Rps7d67OWmxsbNCiRQts2bIFUVFRoqMaTalUokqVKmq1uLi4YN68eYiPjxcdL93+/PNPVT3e3t54+PCh6EgZ9v79e1VNa9asyZLHyHGNSOqb8+uvv8aMGTNw6dKlLOvi0uPGjRv46quv1N6Azs7OyJMnj96VZ8WKFTFlyhT8888/UCgUosvQ8PDhQ1SqVMmoJsuSmpJHjx6hTJkyBuvJkycPRo4cidu3b4uObJQbN27A09NTZz22trbo168fHjx4IDqqSXbt2qW32e/SpQuSkpJExzSJUqlE69atDb4G7ezsMGHCBCiVStGRjXLmzBmtdXh5eWH9+vWQy+WiI5rsw4cPanuw3N3d8e+//4qOlSF3795V1ePp6ZkljWKObES07V1o0aIFlixZglu3bgl/oyYnJ2P27NmwtbUFEaFQoUJISUnB5cuXMWnSJI1G5cslb9686NWrF3bv3o2PHz8KrSWt5ORkTJw4Ue2NuGDBAgwaNAgeHh4W25TExcWhW7duapnz58+vc+u7cuXKWL16tVk9N9q8evXKqCarVatWOH/+vFk+N9ps3bpV43BG6mJtbY2hQ4da1HwsAPj48SMKFy6s8zny9vbGpk2bkJKSIjqqSZo1a6azppIlS+LAgQMW87pL9eUGWa5cueDv7y86VrqdPHlSrZ758+dn+mPkuEakatWqBg9/5M2bF507d8aGDRvw/PlzYS/0Bw8eoEaNGiAijWO9b968wdq1a9G6dWu9hz2sra1Rv359LF68GA8ePDCLN+3Fixfh6+sLIsLWrVsBACkpKThz5ozFNiWSJOHXX39VzUPo378/QkJCsGjRIpQsWVJrLfb29ujevTvOnDkjvPnV5ePHj2jQoIEqs6+vLxo1aqS1nipVqmD37t0WMdht3LhR7zrA2dkZCxYswKdPn0RHNdrNmzdhb2+vs1kMDw8XHdFkN2/eNNgI16hRA9euXRMd1Whjx47VqMHGxgZ//PGH6GjpsnXrVrVaXFxcMn1uUo5rRGJiYhAVFYVDhw5hxIgRKF26tMEXup+fH/r3749du3YhLCwsW3MrFAosW7ZM7xstISEBx44dw9ChQ1UDvL5aUie8ilzJRkVFoWfPnpg2bZrG90xpSn766Sezakr++ecfFCpUCK1bt1bdJkkSLl++jH79+iF37tw6n5dZs2bh9evXAtNrl5SUhB49eqiaDQAICAhAt27dtO718fPzw/Lly81yLlZaq1evVmUuWrQoWrZsqVGLj48Ptm/fbraN4pc2b96s8/3i5eWFU6dOiY5osi/3NqYd8Pr16wd/f3+zOrxuyP/+9z+dz9GyZctExzPZokWLNOoYP358pj5GjmxEvvT27Vts374dvXv3RqFChQw2Jl999RXGjBmDo0ePmt3KVpIk3Lt3DwsXLkTdunX17v3JlSsX2rRpI3TC64sXL/R+3xKbkvfv32PChAlavxcbG4vNmzejdu3aWutIneC6e/dus5rgqlQqMWXKFJQuXVrt9levXmHMmDFaGyw3NzdMmjQJ7969E5TasF9++QVEhEaNGgH4fBZKhQoVtO7tOX/+vOC0xvnhhx/U1lVfHoYaO3asRc2Def78udYznlxdXXH9+nXR8UwWHR2tdb3s6OgIX19f7Ny5U3REk2g7g9DBwSFTx5T/RCOSliRJePLkCVavXo327dvDzc1Nb1NiY2ODZs2aCR/8dPnw4QN27tyJHj16wN3dXW8tFSpUMLvGKi1TmpKnT58KzWrM6+HRo0cYP3488ufPr7WOPHny4Ny5c9mQ1nhHjx7VevvHjx+xcOFCFChQQKMOW1tbsz7LZtGiRWjTpo3qa4VCgS1btqBgwYIatYwcOVJgUuN8+vQJlStXBhHhf//7H86dO6dRS7Vq1SziEFqqESNGaH2PuLq64smTJ6LjmaxatWoaGyCWdHgprS/3WNWuXRuNGzfGiBEjMu0x/nONyJcUCgWuX7+OhQsXomnTplrnYzRv3jyLUmeulJQU/P333zonvJYpU0Z0RKPpa0ry5MljUTPq5XI5Dh8+jLZt26od6rCxsbG4SZNJSUn4/fffUbZsWbXnxNzPFtI2CMTHx2POnDlqe3sOHjwoIJ3pXrx4ATc3NwQGBgIAIiMj0b59e1UdCxYsEJzQNO/fv1edKr9gwQLVGV3du3e3qIYq1fjx40FEqvlXtWrVwr1790THSpemTZti2bJl6NChA8qXL686hTcz9+j+5xuRLyUmJuLcuXOYPHkyatSoASsrKyxevDiTUmavLye8ZvZxvezyZVPSr18/0ZHSLe0E1/bt24uOk26SJMHf3x+NGjVC06ZNRcfJkNDQUAwaNAgNGjQw2z2f2pw4cUJtkJYkCRs3bkTr1q3N8hR/Q2bNmgUnJyckJibi4cOHGDFihEU2IcDn58bPzw9xcXFmPVndGKnNbla+N0wZv2UAQGYqNjaWXF1dKSYmhlxcXDLtfqOjowkA5cmTJ9PuU4TExERKTEwkd3d30VEyRKFQUGxsrMXXAUD1mrV0nz59svgPBiT6/Noy1w9lNAUAi/m8oLTi4uJo5syZ9Msvv4iOkmHx8fH077//UvPmzUVHsQimjN//yUaEMcZY9sgpzSAzjSnjtxl87B5jjLGcipsQZgg3IowxxhgThhsRxhhjjAnDjQhjjDHGhOFGhDHGGGPCcCPCGGOMMWG4EWGMMcaYMNyIMMYYY0wYbkQYY4wxJgw3IowxxhgThhsRxhhjjAnDjQhjjDHGhOFGhDHGGGPCcCPCGGOMMWG4EWGMMcaYMNyIMMYYY0wYbkQYY4wxJgw3IowxxhgTxkZ0AHNw//59+uWXX8ja2prs7e3JwcGBHBwc1P6v62tPT08qU6aM6BK0AkCbNm2ie/fukaurK7m5uaktX95mZ2cnOrLRIiIiaNmyZeTs7EwFChSgggULqv7NmzcvWVlZbo995swZun79OpUoUYJKlixJxYsXJycnJ9GxMkwul9O6devI29ubqlevTj4+PiSTyUTHyhQPHz6kW7duUfPmzcnT01N0nEz1559/qp6vnCQsLIyCgoKoRo0aoqNkumvXrlH16tUtZj0oAwDRIXSJjY0lV1dXiomJIRcXlyx9rBs3blCvXr0oMDDQ6N/JmzcvnTt3jipWrJiFyTJGoVDQjBkzaOHChQZ/NleuXKrmxM/Pj7Zv30758+fPhpTp8+DBA/ruu+/o5cuXarfb2NhQgQIF1BqUtP/38fGhr776SlBqwyRJoilTptDixYtVtxUsWJBKlCihak5S/y1atCg5ODgITGuaJ0+eUMOGDen9+/eUP39+qlatGlWvXl31r6UO4gBo8ODBtGnTJqpatSq1aNGCWrRoQbVq1SIbG8ve3rtz5w59/fXX1KBBAxowYAC1bdvWojZadAFAzZo1Izc3N5o/fz6VKlVKdKRMs2vXLtq1axf98ccflCdPHiEZTBq/YcZiYmJARIiJicmWx4uPj8eQIUNARAaXvHnz4s6dO9mSKzP4+/sjb968RtXm4eGBmzdvio5slA8fPqBp06ZG1UVEcHR0xNGjR0XHNsqvv/4KmUymtx6ZTAY/Pz80a9YMw4YNw6tXr0THNujx48fw9PTUWo+3tzfat2+PBQsW4PTp0/j48aPouEaTy+X45ptv1OpxdXVFp06dsHnzZgQHB4uOmG7Lli1T1ZQvXz6MGzcODx8+FB0rw65fvw4igrW1NQYPHoyQkBDRkTJFbGwsHBwcUKRIEWHrclPGb25EtDh69Cjy5cundwDw8fHB9OnTcf/+fUiSlK350is4OBh16tQxOFivXbsWSqVSdFyjpaSkYOzYsQbr8vLyQkBAgOi4Jtm/fz/s7e0N1mZvb48tW7aIjms0fc3Il0uxYsWwcuVK0ZGNEhMTg6+++kpnLV999RXGjx+Pc+fOISkpSXRcoymVSq0Nf61atbB582bExsaKjphunTt3VttQmTp1KqKjo0XHyrBOnTqp1g2bN2/O9sfnRiQThIWFoU2bNkatKEuXLm0xTYlcLsekSZMM1uTr64upU6fiyZMnoiMbbdu2bXoH7bx582LixIl4+fKl6KgmuXTpEtzc3PQ+X4cOHRId02TGNCPW1taYM2cOUlJSRMc1WlBQEAoWLGjwPZY7d2707NlTyPotPd69ewd3d3edtfzwww/4559/zH4d+KXAwEBYW1trrCt++eUXi2oWv7R//361mvr3749Pnz5l2+NzI5JJJEnC+vXrkStXLqMaEktqSo4fP270oZqaNWti7dq1+PDhg+jYBl27ds3gICCTydCqVSscPXoUCoVCdGSjPHjwAN7e3jprsrW1Rd++ffHo0SPRUU1iqBlp3769xQzUad26dQu5c+fW+zrs3r073r17JzqqSf7880+D64syZcpgyZIliIiIEB3XaEOHDtVai5+fH7Zv324x64m0EhIS4OTkpFZP5cqV8eLFi2x5fG5EMtmTJ09QtWpV1ZPZr18/HD16FL1794aLi4vFNiVBQUH4+uuv1QbosWPH6hwY7Ozs0KFDBxw5cgTJycmi4+sUEhKCWrVqqWV3dHTUuaJZsGAB3r9/Lzq2QcHBwShfvrzBgeC7777DlStXRMc1mqFmxMPDAytWrLC4rdNjx47ByspK57rh+fPnoiOmy8CBA/W+/vz8/LB27VokJiaKjmq00NBQnesIIkKFChVw/Phxs1yP69OjRw+NWtzc3LJlnhw3IllALpdj6tSpsLKyQpMmTVS3JyUlWXRTIpfLMWHCBFXO8PBwpKSk4Pjx4+jatavOQx0eHh4YOXIkAgICzKqeVElJSfjhhx9UeTds2ICTJ0/i22+/1To42Nraonv37vjrr7/Msp5UUVFRaNiwodoWjq7JuvXr17eYlacxh2kKFy6MHTt2WNT8pTVr1uisJ1euXFi8eLFFHXYCPk/qL1mypM71nDmsr9Nj+vTpBpv8du3aIT4+XnRUox05ckRnLdOmTcvSPT05rhEpXrw4fvrpJ/z111/C37SXL19Gw4YNtX7PkpuSY8eOwd3dXWOGdVRUFDZu3Ii6devqrKds2bJYtGgR3r59Kyi9dpIkYdWqVbC2tsaiRYtUt7958wZTp07VOfCVL18ea9asMdsValJSErp06aJaMQJAQEAAOnfurPUsmwoVKmDnzp3C3zuGpG1GSpcujX379qF48eIa9VSsWBEnT540m/eOIePGjVNreG1sbNTqqVSpksVNog4ICNCoI+3zY4l7e2JiYuDh4aG1prZt2+L48eNmvSdYm6SkJLi6uupcdzdt2hTh4eFZ8tg5rhFJu+TNmxe9e/fGgQMHhM3UjouLM/gzltiUBAUF6Z2c+vz5c8yaNQtFixbVWotMJkOzZs3wxx9/mNVWw7lz57B48WKN25OTk7F37140aNBAaz1OTk4YMmQI7t69KyC1fkqlEmPHjkXLli3Vbg8MDMSgQYNgZ2endY/CqlWrkJCQICi1YanNSOXKlQF83mO3du1arU1j48aNcf36dcGJDVMqlejQoYOq6bh79y6qV6+uVouVlRXGjRtnVu8bQxYtWqTK/+U6ztXV1WJOk09rxYoVWtcF5cqVs4jDt9r07dtX716eokWLZsm8kRzdiKRd7Ozs0KJFC6xdu9asz9G3xKZEH0mScPnyZQwcOFBnPU5OTujbty/Onz9vFrvSDWV4+PAhRo4cqbOeOnXqYMeOHWY3T+HSpUtabw8JCcHEiRO11uPh4YG5c+ea7eTjx48fo3379mq3xcXFYe7cuXB2dtaop3PnzggMDBSU1jgJCQmoUaMGWrVqBQBQKBRYsWKFxoRWPz8/nDhxQnBa4ygUCtVhwmnTpmHbtm1wcHBQq2fq1KkWNdEzKSkJhQsXVmsQLb0ZOXnypNZ1Wr9+/fD48WPI5fIsedwc14gcOXIEo0aNgp+fn97GpEqVKpg1axZu3rxptgN5TmtKPn36hD179qBVq1Yap8ClLpZ0KnBcXBw2btyISpUqaa3Fw8PDok4Bjo6OxqJFi+Dl5aVRS+7cuTF27FizbOJ17e0MDw/H6NGjYWtrq1aLjY0Nhg4ditDQ0GxOarywsDDMnz9f7bbXr1+jVatWGs9Njx49smyXeWYKCgqCm5ub6vTxO3fuaOwxbdasmUWdQbNjxw5V43HgwAG1Q1CW2IzI5XKtZ0i6uLhk6QUQc1wjklqIJEm4d+8e5s2bhxo1auhtSry9vTF06FCcOHHC7LZiU+W0piQ0NBS//PILKlasqLMWSzkVWJIkXLlyBb1799Y6YdfSTgFOTEzEhg0btM65sMRTf1++fImePXtqzIlxdHTE9OnTzXZ+j7b3ryRJ2LNnD/Lnz69Wi7u7O7Zu3WrW73kA2LdvH4KCglRff/z4UeMaTL6+vhZxGA34vPe0YsWKmDVrFgDkiGZk0KBBICL07NkTpUqVUtvTm1Vzx3JsI/KlkJAQbNy4EW3atNHYJfjlYYKOHTti27ZtZtuZ57Sm5M6dO/jxxx+NOhU4q3YNZpbIyEgsWbIExYoV01qLJZ0CrFAosG/fPrXT0dMulnbq7+3bt9GiRQute65Wrlxpthsh2nz48EHtTK/UpWnTphY3+VOpVGLevHlqjaKdnR3Wr19v1uutVCdPnlS7hL2lNyPnz5+Hvb09goODcevWLbU9inPmzMmSx/zPNCJpJSQk4MiRI+jfv7/GlkXaxcrKCvXq1cOSJUvMdkvW1KbEXLf+gM+XX/f390e3bt10NoseHh4YNWqU2Z118yWlUomTJ0/iu+++03sKsCV8BockSTh79qzeU38vX74sOqbRzp07h2rVqmnUUbhwYezbt090PJOcP39eY89V6qm+ljCIp3X69GmNwwK9e/fO1it8poe2v7MlNyMKhQJLly5Vfb1kyRJVHdbW1vj3338z/TH/k41IWkqlEleuXMHkyZNRrlw5rSvaMmXKZFHqzGWoKXF1dbWYU8qio6OxadMm1KtXT2uDaEkfOBUUFIRp06ZpnXtx7do10fFMouvU3127domOZhJJkrSe8jt79mzR0Uz26dMnTJ48WW3g69Kli+hY6fLmzRu1s4QqVqxo1mdu6ZO2GfHw8MD9+/dFRzJa2uZKqVSiSZMmIPo8v2rjxo2Z/nhm1YgkJSWp5gzcvn3bpN/NrAuaPX/+HMuXL0fjxo1VEyonTJiQofsUQVtT0qdPH9Gx0uXFixdqpwK3aNFCdKR0kcvl2Ldvn+rsgapVq1rcVmuqtKf+FilSxOyvO6JL2lN+8+fPb9Tp9uYq9VTfPHnyICwsTHScdEtKSsLgwYPh6upqcYeZvnTgwAEUKFDALE/rN8Xbt29Ru3btLLuGjSnjtwwAKAuNHj2anj17RidOnKDbt29TpUqVjP7d2NhYcnV1pZiYGHJxccmUPFFRUXTy5EmqWLEilS1bNlPuU4Tk5GQ6c+YMFSpUiCpXriw6TroBoH///ZdsbW2pRo0aouNkyKNHjygmJoZq164tOkqGhIaG0uvXry2+jvj4eHry5AlVq1ZNdJQMUSqV9OTJEypXrpzoKBn29u1b8vb2Fh0jwz59+kSOjo6iY2QYAJLJZFly36aM31naiJw4cYLGjRtHBw8epHLlyplFI8IYY4yxrGXK+G2TVSHev39PAwcOpMOHDxvdOSYnJ1NycrLq69jY2KyKxxhjjDEzYJUVdwqA+vbtS0OGDDFpt+jChQvJ1dVVtfj4+GRFPMYYY4yZCZMakUmTJpFMJtO7PHnyhFatWkVxcXE0efJkk8JMnjyZYmJiVEtwcLBJv88YY4wxy2LSHJGIiAj68OGD3p8pWrQodenShY4ePao2CUapVJK1tTX17NmTtm3bZtTj8RwRxhhjzPIIn6waFBSkNr8jJCSEvvnmGzpw4ADVrFnT6FnT3Igwxhhjlkf4ZFVfX1+1r52cnIiIqFixYjni1C3GGGOMZY4smazKGGOMMWaMLDt9N63ChQtTFl83jTHGGGMWiPeIMMYYY0wYbkQYY4wxJgw3IowxxhgThhsRxhhjjAnDjQhjjDHGhOFGhDHGGGPCZMvpuyLdvHmTJkyYQADIxcWFnJ2dycXFRevy5fdcXV0pV65cokvQSpIkWr58OZ04cYLy5cund3F3dycrK8vpOUNDQ2nChAlEROTj46NafH19ycfHh9zc3NQ+PsCS/O9//6Ndu3ZRqVKlVEvJkiXJ2dlZdLQMSUpKopkzZ5KtrS1VrVqVqlSpQr6+vhb7PKV17949+v3336l+/frUoEEDyps3r+hImQIArV69mlxdXalt27aUJ08e0ZEyzfv372nr1q3Up08f8vLyEh0nUx06dIiKFStGFSpUEB0l02TJJd4zS2Zd4v3ly5fUrVs3unHjhtG/kzt3bjp69Cg1atQo3Y+b1QDQ2rVracyYMaRQKHT+nJWVFeXNm5c8PDwoX758VKRIEVqxYgW5ubllX1gThYaG0nfffaf1OcudO7dag5K2SSlSpAgVL15cQGLjbdiwgYYNG0aSJKluK1iwoFpzkrr4+fmRtbW1wLTGi4yMpCZNmtC9e/eIiMjDw4OqVKlCVapUoapVq1LVqlWpcOHCFtmcrF27loYPH04ymYwqVKhAjRs3pkaNGlH9+vXJ1dVVdLx0+/DhA1WrVo3evn1LTZo0oY4dO1K7du0oX758oqNl2Jw5c2ju3LnUsWNHGj58ONWtW9ciX3tfCgkJoZIlS1KHDh1ozpw5VLhwYdGRtDJp/IYZi4mJAREhJiYmw/eVnJyMH3/8EURkcHF1dcW///6bCRVkj3/++QcFChQwqjYPDw9cu3ZNdGSjfPr0CV27djWqrtTn7cyZM6JjG+XQoUOwt7c3WJO9vT3KlSuHLl264N27d6JjGxQZGYlKlSrprCdPnjxo0qQJJkyYgD179uDZs2eQJEl0bKPMmDFDox4rKytUq1YN48ePh7+/P2JjY0XHNNnt27eRK1cutZoaNWqE1atXW8RrThe5XI4qVaqo6vrqq6+wbt06xMXFiY6WYVOmTAERwc7ODmPHjkVERIToSBpMGb//M41IqmPHjiFv3rx6V/41atTAoUOHkJSUlGmPm9VCQ0NRv359vXXJZDKcOHFCdFSTSJKEWbNmGRywixYtikePHomOa5LLly/Dzc3NYG358+fHxYsXRcc12ocPH1C1alWjmkdra2usWrVKdGSjSJKEwYMHG6ynVq1amDx5Mk6fPo1Pnz6Jjm2UnTt36lxnfP3111i2bBlev34tOqbJ7t+/Dzs7O7WanJ2dMWLECItbX6QVHR0Nd3d3VU0uLi6YP38+4uPjRUdT4UbEgODgYNSrV8/gSjJPnjwYPHgwLl++bBFbbXK5HOPGjTNYV5MmTbB7926LarT27t0LBwcHnTUVLFgQ8+fPR3h4uOioJrl//z4KFSqksy4rKyucPHlSdEyTRUVFoXr16gabxytXroiOahKFQoGOHTsa1WCNHz8eCQkJoiMbzZh1R7Vq1bBw4UK8ePFCdFyjLVy4UGc9jRo1woEDByCXy0XHNNkvv/yiUU+BAgWwYcMGpKSkiI7HjYgxUlJSMH36dMhkMqO23AoXLoxp06bh8ePHmZ4ls+3Zswe5c+c2WJO7uzvGjBmDBw8eiI5slOvXrxs8BGVvb4++ffvi1q1bouMa7c2bNyhTpozeutq2bWtxg3Z0dDRq1aqls6aqVavi/PnzomOaLCkpCY0aNdJZl5eXl0W9/lKlpKSgcePGel+HMpkM/fr1Q3BwsOi4RktJSUHNmjX11lWwYEHMnj0bISEhouMaLSkpCX5+flrrKVmyJA4cOCB0A5obEROcPXsWXl5eqidwypQpmD17NkqUKKF3q2DFihUICwvLslwZ9eDBA5QsWVJt5di+fXvY2NhoralWrVr47bffzP746du3b9WO+xIRnJyctNZUt25d7N271yK2diIjI1G7dm2DzWPDhg1x6tQpi9hDB3x+D3/99dd6a2rWrBkCAgJERzVJTEwMKleurLOmli1b4tmzZ6JjmiwiIkLn4GZtbY2zZ8+Kjpgujx8/1rtHNfW9ZWmHrrdv3663pho1agg7rMuNiInCwsLQvHlzEBGmT58O4PPx4GvXrmHkyJHIly+fzjdmy5YtsXPnTrM6NpcqOjoa7dq1AxGhUKFCAD7PJVm8eLHORsvJyQkDBw7EtWvXzHawi4+PV9s9fubMGezduxd169bVWlOhQoUs4rBNQkIC2rRpo8rdokULdO3aFVZWVlr3Jhw4cABKpVJ0bINiY2PVnht7e3u1yZGpS6dOnfDkyRPRcY0WFhaGYsWK6RwE7OzsMH36dIs6PAMAt27d0jlo58uXD4cPHxYdMV2WLVum87k6ePCg6HjpolAoUKFCBb3NiIuLC3bt2pXt2bgRSQelUomFCxeif//+Gt+Ty+U4fvw4unXrpvMNmjt3bnz//fc4deoUFApFluc1liRJWLRoEezt7dUGLUmScOnSJXz//fc6a/rqq6+wcuVKfPjwQWAF2imVSkybNg1EpLZivHnzJvr27av1jBRLOGyTkpKCH374AUSEQYMGAQCePXuGgQMHwtbWVqOmUqVK4ffff0dycrLg5PrFxcWhQYMGIPq82zgkJATDhg3T2ENnbW2NAQMGWMyu/xcvXsDT01OVf/DgwRqNo5+fHw4fPmy2jb02f/zxh97BrV+/ftmyXs5MCoVC58aKh4eHRU0IT+v48eM6x6Q///xT2FxAbkQywNDhlpiYGGzduhVNmzbVOb/Ey8sL48aNw61bt8xm5XPmzBmde20+fvyI1atXo2LFilrrsbe3R48ePXD+/Hmz2wLfuXMn9u7dq3F7eHg45s+fr3MiqDkftpEkCVOnTkW/fv3Ubn/79i3GjRundf6Pj48PVq5cadZb3/Hx8WjcuDHKly+vuu358+fo2bOnxnvJ3t4eP/74o1melvil27dvw8XFBXZ2dpAkCXfu3NE64Fna4ZoxY8aosh8+fBi+vr5q9RQuXBiXLl0SHdMkz58/h6Ojo9rrLPX/NjY2WLt2reiIJpMkSdXkf7l07txZ2DqOG5Fs8vbtWyxZskTnAE5EKFu2LBYsWGARp75JkoSAgAAMGTIEzs7OWuspVqwYFixYYFaTuvQ1R3K5HPv27bPIwzYPHz7UentkZCRmzZqFPHnyaN2ymzt3Lj5+/JjNaY2TkJCAiRMnatx+9+5dtcNSqYuzszNmz55t9tfnuHDhAooWLar6WpIkbN++XW1vCZFlHa5JSUlBw4YNkS9fPgCfD/X26dNHrR6ZTIbx48db1Bl4q1evVu2Zu379OgoWLKhW05AhQ8x+D+OXrl69qsqf9rRekc1IjmtEzHlXeqp79+5h4sSJ8Pb21tmU1K9fHxs3bjTbQSKt+Ph4bNmyBXXq1NFai7W1Nb777jscPXrULE4VM4alH7b5UlxcHJYtW6axIk0dwCdMmIDQ0FDRMTXo20t4+fJlrU1jvnz5sHLlSrMe8LS9dqKjozF69GiLPVwTHh6Obt26qd32559/wsPDQ62er776Cnfv3hWU0jRKpRKNGjVC3759AQAhISEaZ9XUr1/fLDdO9EmdN7dz505MnDhReDOS4xoRIkLlypWxYMECs9+1qVQqceHCBfzwww9wcXHROojb2dmhY8eOFnPRtEePHmHcuHEaK5/UpWDBgpg6darFXFvAkg/baJOUlISNGzeiePHiWhusIUOGWMxzA3xuVI4fP651Ep6fnx+2bt1qVvOwjKHrcE2rVq3Mfp2mbe9NaGioxh4sW1tbLF682CKem1evXmH37t2qrxMTEzX29vj5+eHOnTsCU5rmyZMncHJyQmxsLCRJEt6M5MhGJO1iKU3Jp0+fsG/fPnz77bc6T5u1pIumJSUlYd++fWjevLnO+TGWdLE0Sz5so41CocCePXu0Hiq0trZGz549cf/+fdExjaZUKrFr1y6tZ6aULVsWhw4dMvv3TFo54XBNWpIkYePGjRpzlurVq4eXL1+KjmfQl68dSZLwyy+/qO29cnR0xIEDBwQlNN2xY8dU/xfdjOS4RkTf+d+W0pRERERg7dq1eq8VYUkXTXv16hVmzJih81CUpV0sLScdtkndo6CrwbK0i6PJ5XKsW7dO68XsatasaXEXRbP0wzVfev78uca1YpycnPDbb79ZXC0AcPLkSY2PXpg5c6bZTdQ3hshmJMc1IiEhIdi3bx86deqk9foDltaUPH/+PEdcNA34vBV+/PjxHHGxNCDnHba5fPkyWrVqpbUWS7s4WkJCAhYtWqT183ks8aJolny45ksKhQILFy7UOMX822+/xfv370XHM9nTp09RqlQptVo6dOhgEeuwL4lqRnJcI5K2kPj4+BzTlKS9aJqu+RfmftG0tHLCxdJS5bTDNrdv384RF0cDPp9uPnny5BxxUbScdrjm9u3bKFeunFotlnoRtOjoaI0mvkKFCnj16pXoaCYT0Yzk6EYkrZzUlMjlchw7dswiL5r2JUmScPHiRfTq1csiL5b2pVu3bqFfv3454rBNYGAgBgwYYNEXR0ul76Jo/fv3R1BQkOiIRstJh2sSExPx448/aswj++GHH8z2Ugy6KBQKjQHcUi9+lt3NyH+mEUkrJzUlqRdNa9KkiUVdNE0bS75Y2pdy0mEbS784Wlr6Loo2btw4i7goWqq7d+/mmMM1Fy5c0HoRtL/++kt0NJPt2LFDbaPKki9+ll3NyH+yEUnLmKbExcXFIrb8DF00TSaTmdXFxXSRJAk3btzA4MGDdV4s7erVq6JjGsXQYRsRn+uQXpGRkZg5c6bWi6PNmTNHdDyT6Loo2vfffy86mkl0Ha6pVq2aWW90aKPtImgeHh5mf5hZmy8vfmZtbY1Hjx6JjmUybc3Izp07M/1x/vONSFq6mpJevXplYtLsoe2iaU2aNBEdy2TaLpZWpkwZi1vJApqHbfLnz28Rpy5/6cuLozk6OlrUnoS00l4Uzdra2qLmjKT15eEaS9yTkCrtRdC0fSSDpQgJCUGtWrVARFi5cqXoOOmWthmZOHFilqx7TRm/ZQBAZio2NpZcXV0pJiaGXFxcMnx/CQkJ5O/vT/v27aP+/ftTixYtMiFl9pMkif766y/6448/qHnz5tS1a1fRkdLt8ePH9Ntvv1GZMmWof//+ouOkW0REBG3atImcnJxo1KhRouOkW3JyMm3fvp2ioqJowoQJouOkGwA6ceIE3b17lyZPniw6Tobcu3ePTpw4QRMnThQdJUPCwsJoz549NGbMGNFRMiQpKYn27NlDffr0IZlMJjpOugGgU6dO0TfffJMldZgyfv+nGhHGGGOMZT1Txm+rbMrEGGOMMaaBGxHGGGOMCcONCGOMMcaE4UaEMcYYY8JwI8IYY4wxYbgRYYwxxpgw3IgwxhhjTBhuRBhjjDEmDDcijDHGGBOGGxHGGGOMCcONCGOMMcaE4UaEMcYYY8JwI8IYY4wxYWxEB9An9YOBY2NjBSdhjDHGmLFSx+3UcVwfs25E4uLiiIjIx8dHcBLGGGOMmSouLo5cXV31/owMxrQrgkiSRCEhIeTs7EwymUx0HOFiY2PJx8eHgoODycXFRXScHIv/ztmD/87Zg//O2YP/zuoAUFxcHBUsWJCsrPTPAjHrPSJWVlbk7e0tOobZcXFx4Rd6NuC/c/bgv3P24L9z9uC/8/8xtCckFU9WZYwxxpgw3IgwxhhjTBhuRCyIvb09zZw5k+zt7UVHydH475w9+O+cPfjvnD3475x+Zj1ZlTHGGGM5G+8RYYwxxpgw3IgwxhhjTBhuRBhjjDEmDDcijDHGGBOGGxELl5ycTJUqVSKZTEZ37twRHSdHef36NfXv35+KFClCuXLlomLFitHMmTNJLpeLjpYjrFmzhgoXLkwODg5Us2ZNun79uuhIOcrChQupevXq5OzsTPnz56d27drR06dPRcfK8RYtWkQymYzGjBkjOorF4EbEwk2YMIEKFiwoOkaO9OTJE5IkiTZs2EAPHz6k5cuX0/r162nKlCmio1m8vXv30rhx42jmzJl069YtqlixIn3zzTcUHh4uOlqOcenSJRo+fDhdvXqVzpw5QykpKdS8eXNKSEgQHS3HunHjBm3YsIEqVKggOoplAbNY/v7+KF26NB4+fAgiwu3bt0VHyvF+/vlnFClSRHQMi1ejRg0MHz5c9bVSqUTBggWxcOFCgalytvDwcBARLl26JDpKjhQXF4cSJUrgzJkzaNCgAUaPHi06ksXgPSIW6v379zRw4ED6448/yNHRUXSc/4yYmBhyd3cXHcOiyeVyunnzJjVt2lR1m5WVFTVt2pSuXLkiMFnOFhMTQ0TEr98sMnz4cGrdurXa65oZx6w/9I5pB4D69u1LQ4YMoWrVqtHr169FR/pPeP78Oa1atYqWLl0qOopFi4yMJKVSSZ6enmq3e3p60pMnTwSlytkkSaIxY8ZQnTp1qHz58qLj5Dh79uyhW7du0Y0bN0RHsUi8R8SMTJo0iWQymd7lyZMntGrVKoqLi6PJkyeLjmyRjP07p/Xu3Ttq0aIFde7cmQYOHCgoOWPpM3z4cHrw4AHt2bNHdJQcJzg4mEaPHk07d+4kBwcH0XEsEl/i3YxERETQhw8f9P5M0aJFqUuXLnT06FGSyWSq25VKJVlbW1PPnj1p27ZtWR3Vohn7d7azsyMiopCQEGrYsCHVqlWLtm7dSlZW3L9nhFwuJ0dHRzpw4AC1a9dOdXufPn0oOjqajhw5Ii5cDjRixAg6cuQI/fXXX1SkSBHRcXKcw4cPU/v27cna2lp1m1KpJJlMRlZWVpScnKz2PaaJGxELFBQURLGxsaqvQ0JC6JtvvqEDBw5QzZo1ydvbW2C6nOXdu3fUqFEjqlq1Ku3YsYNXKJmkZs2aVKNGDVq1ahURfT504OvrSyNGjKBJkyYJTpczAKCRI0fSoUOH6OLFi1SiRAnRkXKkuLg4evPmjdpt/fr1o9KlS9PEiRP5UJgReI6IBfL19VX72snJiYiIihUrxk1IJnr37h01bNiQ/Pz8aOnSpRQREaH6npeXl8Bklm/cuHHUp08fqlatGtWoUYNWrFhBCQkJ1K9fP9HRcozhw4fTrl276MiRI+Ts7ExhYWFEROTq6kq5cuUSnC7ncHZ21mg2cufOTXnz5uUmxEjciDCmw5kzZ+j58+f0/PlzjQaPdyRmTNeuXSkiIoJmzJhBYWFhVKlSJTp58qTGBFaWfuvWrSMiooYNG6rdvmXLFurbt2/2B2JMBz40wxhjjDFheNYdY4wxxoThRoQxxhhjwnAjwhhjjDFhuBFhjDHGmDDciDDGGGNMGG5EGGOMMSYMNyKMMcYYE4YbEcYYY4wJw40IY4wxxoThRoQxxhhjwnAjwhhjjDFhuBFhjDHGmDD/DwIUja4/f9P5AAAAAElFTkSuQmCC", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# b)\n", + "u = 2*X + 4*Y\n", + "v = -2*Y\n", + "\n", + "plt.quiver(X, Y, u, v)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "2f923026-756b-48aa-8b57-0263f2012cc6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "<mpl_toolkits.mplot3d.art3d.Line3DCollection at 0x7f9bfe649a10>" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# c)\n", + "X, Y, Z = np.meshgrid(x, x, x)\n", + "u = -1*X - 3*Y\n", + "v = 2*Y\n", + "w = -1*Z\n", + "\n", + "ax = plt.figure().add_subplot(projection='3d')\n", + "\n", + "ax.quiver(X, Y, Z, u, v, w, length=0.1, color = 'black')" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "84f34473-ad8d-471c-818b-019739c4ce45", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "<mpl_toolkits.mplot3d.art3d.Line3DCollection at 0x7f9bfe649990>" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# d)\n", + "X, Y, Z = np.meshgrid(x, x, x)\n", + "u = -2*X - 3*Y\n", + "v = -1*Y\n", + "w = -1*Z\n", + "\n", + "ax = plt.figure().add_subplot(projection='3d')\n", + "\n", + "ax.quiver(X, Y, Z, u, v, w, length=0.1, color = 'black')" + ] + }, + { + "cell_type": "markdown", + "id": "e17e504e-5d4e-4aa1-be5c-5c92bc3b3b81", + "metadata": {}, + "source": [ + "# Exercise 4" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "c2f0426b-34a1-406d-9933-1a4bbf1196a3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "<matplotlib.quiver.Quiver at 0x7f9bf7d799d0>" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#a)\n", + "x = np.linspace(-1, 1, 10)\n", + "X, Y = np.meshgrid(x, x)\n", + "u = -1*X\n", + "v = -1*Y\n", + "\n", + "plt.quiver(X, Y, u, v)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "8b7de4a3-bb67-479f-ba47-e7ed5b7883dd", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "<matplotlib.quiver.Quiver at 0x7f9bf7153d10>" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#4c)\n", + "\n", + "x = np.linspace(-1, 1, 20)\n", + "X, Y = np.meshgrid(x, x)\n", + "\n", + "B = np.array([[0, 1], [0, 0]])\n", + "P = np.array([[-1, 1], [2, 1]])\n", + "A = P@B@np.linalg.inv(P)\n", + "\n", + "u = A[0, 0]*X + A[0, 1]*Y\n", + "v = A[1, 0]*X + A[1, 1]*Y\n", + "\n", + "plt.quiver(X, Y, u, v)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "59a4fee3-5c15-4c4e-9990-82efbb525310", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0.13533528, 2.71828183],\n", + " [2.71828183, 0.13533528]])" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = np.array([[-1, 1], [0, -1]])\n", + "np.exp(A + A.T)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "4c710da5-9ee0-4e0b-83e3-770ac395c66f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "<matplotlib.streamplot.StreamplotSet at 0x7fe741b27d90>" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-2, 2, 100)\n", + "X, Y = np.meshgrid(x, x)\n", + "\n", + "# a)\n", + "dx = X*(1-X)*(X-Y)\n", + "dy = Y*(1-Y)*(2*X-1)\n", + "\n", + "color = dy\n", + "lw = 1\n", + "plt.streamplot(X, Y, dx, dy, color=color, density=2, cmap='jet', arrowsize=0.5)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f290b5b1-3bc5-4700-9aee-755cd732290d", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "25540a57-c369-490d-9802-7cbe35698fd6", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "py3", + "language": "python", + "name": "py3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/dyn_sys/script.pdf b/dyn_sys/script.pdf Binary files differ. diff --git a/dyn_sys/sheets/DSNDE_exam_4_6_2023.pdf b/dyn_sys/sheets/DSNDE_exam_4_6_2023.pdf Binary files differ. diff --git a/dyn_sys/sheets/exercises_pt1.pdf b/dyn_sys/sheets/exercises_pt1.pdf Binary files differ. diff --git a/dyn_sys/sheets/exercises_pt2.pdf b/dyn_sys/sheets/exercises_pt2.pdf Binary files differ. diff --git a/dyn_sys/sheets/exercises_pt3.pdf b/dyn_sys/sheets/exercises_pt3.pdf Binary files differ. diff --git a/dyn_sys/sheets/solutions.pdf b/dyn_sys/sheets/solutions.pdf Binary files differ.