\begin{itemize} \item<1-3> Objectives: ``similar behaviors'' in asynchronous iterations as in some chaotic iterations \item<2-3> Issues: \begin{itemize} \item Strengthening the convergence conditions of chaotic mode \item Lightly introduce synchronism into asynchronous modes [ABCVS05] \end{itemize} \item<3> \alert{Proof of convergence conjecture} \end{itemize}