pch, section 6

[16dcc.git] / chaos.tex

diff --git a/chaos.tex b/chaos.tex
index 122c0adce085a17e4da6b6f10a0ab3d1299fc1a6..511a11acab24bdb7d8554928d7afb8cf1c2f5afa 100644 (file)
--- a/chaos.tex
+++ b/chaos.tex
@@ -247,7 +247,7 @@ $\check{u}^{v^0}$ (on $n$ digits), ..., $\check{u}^{\check{v}^0-1}$ (on $n$ digi
 
 
 \begin{xpl}
 
 
 \begin{xpl}

-Consider for instance that $\mathsf{N}=13$, $\mathcal{P}=\{1,2,11\}$ (so $\mathsf{p}=3$), and that
+Consider for instance that $\mathsf{N}=13$, $\mathcal{P}=\{1,2,11\}$ (so $\mathsf{p}=2$), and that

 $s=\left\{
 \begin{array}{l}
 u=\underline{6,} ~ \underline{11,5}, ...\\
 $s=\left\{
 \begin{array}{l}
 u=\underline{6,} ~ \underline{11,5}, ...\\


@@ -425,7 +425,7 @@ $\mathcal{P}=\{2,3\}$. The graphs of iterations are given in
 The \textsc{Figure~\ref{graphe1}} shows what happens when 
 displaying each iteration result.
 On the contrary, the \textsc{Figure~\ref{graphe2}} explicits the behaviors
 The \textsc{Figure~\ref{graphe1}} shows what happens when 
 displaying each iteration result.
 On the contrary, the \textsc{Figure~\ref{graphe2}} explicits the behaviors

-when always applying 2 or 3 modification and next outputing results. 
+when always applying either 2 or 3 modifications before generating results. 

 Notice that here, orientations of arcs are not necessary 
 since the function $f_0$ is equal to its inverse $f_0^{-1}$. 
 \end{xpl}
 Notice that here, orientations of arcs are not necessary 
 since the function $f_0$ is equal to its inverse $f_0^{-1}$. 
 \end{xpl}


@@ -521,7 +521,7 @@ and only if its iteration graph $\Gamma_{\mathcal{P}}(f)$ is strongly connected.
   In this context, $\mathcal{P}$ is the singleton $\{b\}$.
   If $b$ is even, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach 
   its neighborhood and thus $\Gamma_{\{b\}}(f_0)$ is not strongly connected. 
   In this context, $\mathcal{P}$ is the singleton $\{b\}$.
   If $b$ is even, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach 
   its neighborhood and thus $\Gamma_{\{b\}}(f_0)$ is not strongly connected. 

-  If $b$ is even, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach itself 
+  If $b$ is odd, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach itself 

   and thus $\Gamma_{\{b\}}(f_0)$ is not strongly connected.
 \end{proof}
 
   and thus $\Gamma_{\{b\}}(f_0)$ is not strongly connected.
 \end{proof}
 


@@ -530,4 +530,9 @@ functions and a iteration number $b$
 such that $\Gamma_{\{b\}}$ is strongly connected.
 
 
 such that $\Gamma_{\{b\}}$ is strongly connected.
 
 

- 
\ No newline at end of file
+%%% Local Variables:
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