X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/d69591c41135e899d27072006db6af016df62445..705f6ebe2219797761eb1fd336de90f287787a29:/chaos.tex

diff --git a/chaos.tex b/chaos.tex
index d5ab5f9..511a11a 100644
--- 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}
-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}, ...\\
@@ -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
-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}
@@ -521,12 +521,18 @@ 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. 
-  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}
 
-The next section shows how to generate functions and a iteration number $b$
+The next section recalls a general scheme to produce
+functions and a iteration number $b$
 such that $\Gamma_{\{b\}}$ is strongly connected.
 
 
- 
\ No newline at end of file
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End: