%0 Journal Article
%T On gradient-like random dynamical systems
%A Hmissi Aya
%A Hmissi Farida
%A Hmissi Mohamed
%J ESAIM : Proceedings
%D 2012
%I EDP Sciences
%R 10.1051/proc/201236018
%X This paper deals with some characterizations of gradient-like continuous random dynamical systems (RDS). More precisely, we establish an equivalence with the existence of random continuous section or with the existence of continuous and strict Liapunov function. However and contrary to the deterministic case, parallelizable RDS appear as a particular case of gradient-like RDS. The obtained results are generalizations of well-known analogous theorems in the framework of deterministic dynamical systems. Cet article est consacr¨¦ ¨¤ quelques caract¨¦risations des syst¨¨mes dynamiques al¨¦atoires (SDA) du type gradient. Plus pr¨¦cis¨¦ment, nous montrons que cette notion est ¨¦quivalente ¨¤ l¡¯existence d¡¯une section al¨¦atoire continue ou ¨¤ l¡¯existence d¡¯une fonction de Liapunov stricte et continue. Mais, contrairement aux syst¨¨mes dynamiques d¨¦terministes, les SDA parall¨¦lisables apparaissent comme un cas particulier des SDA du type gradient. Les r¨¦sultats obtenus g¨¦n¨¦ralisent des th¨¦or¨¨mes bien connus dans le cadre d¨¦terministe.
%K Random dynamical system (RDS)
%K Translation
%K Cocycle
%K Random homeomorphism
%K Gradient-like RDS
%K Random section
%K Liapunov function
%K Parallelizable RDS
%K Backward cocycle
%K Syst¨¨me dynamique aleatoire (SDA)
%K Translation
%K Cocycle
%K Homomorphisme aleatoire
%K SDA du type gradient
%K Section aleatoire
%K Fonction de Liapunov
%K SDA parall¨¦lisable
%K Cocycle backward
%U http://dx.doi.org/10.1051/proc/201236018