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[book_gpu.git] / BookGPU / Chapters / chapter18 / ch18.tex

diff --git a/BookGPU/Chapters/chapter18/ch18.tex b/BookGPU/Chapters/chapter18/ch18.tex
index d161c762743db39f988c5184b14a94ae4f4b22b0..7c2a3931d7f91c39a8f01f39ecb8d4e59bb1d50b 100755 (executable)
--- a/BookGPU/Chapters/chapter18/ch18.tex
+++ b/BookGPU/Chapters/chapter18/ch18.tex
@@ -93,7 +93,7 @@ with basic notions on topology (see for instance~\cite{Devaney}).
 
 
 Chaos theory studies the behavior of dynamical systems that are perfectly predictable, yet appear to be wildly amorphous and meaningless. 
 
 
 Chaos theory studies the behavior of dynamical systems that are perfectly predictable, yet appear to be wildly amorphous and meaningless. 

-Chaotic systems\index{chaotic systems} are highly sensitive to initial conditions, 
+Chaotic systems\index{chaotic!systems} are highly sensitive to initial conditions, 

 which is popularly referred to as the butterfly effect. 
 In other words, small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes, 
 in general rendering long-term prediction impossible  \cite{kellert1994wake}. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved \cite{kellert1994wake}. That is, the deterministic nature of these systems does not make them predictable \cite{kellert1994wake,Werndl01032009}. This behavior is known as deterministic chaos, or simply chaos. It has been well-studied in mathematics and
 which is popularly referred to as the butterfly effect. 
 In other words, small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes, 
 in general rendering long-term prediction impossible  \cite{kellert1994wake}. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved \cite{kellert1994wake}. That is, the deterministic nature of these systems does not make them predictable \cite{kellert1994wake,Werndl01032009}. This behavior is known as deterministic chaos, or simply chaos. It has been well-studied in mathematics and


@@ -149,7 +149,7 @@ When $f$ is chaotic, then the system $(\mathcal{X}, f)$ is chaotic and quoting D
 
 
 
 
 
 

-\subsection{Chaotic iterations}\index{chaotic iterations}
+\subsection{Chaotic iterations}\index{chaotic!iterations}

 \label{subsection:Chaotic iterations}
 
 Let us now introduce an example of a dynamical systems family that has
 \label{subsection:Chaotic iterations}
 
 Let us now introduce an example of a dynamical systems family that has