Abstract. 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.MSC (2000): Primary: 37H10. Secondary: 39B52, 37B25, 37B35 Keywords: Random dynamical system (RDS), Translation, Cocycle, Random homeomorphism, Gradientlike RDS , Random section, Liapunov function, Parallelizable RDS, Backward cocycle.
Résumé. Cet article est consacréà quelques caractérisations des systèmes dynamiques aléatoires(SDA) du type gradient. Plus précisément, nous montrons que cette notion estéquivalenteà l'existence d'une section aléatoire continue ouà l'existence d'une fonction de Liapunov stricte et continue. Mais, contrairement aux systèmes dynamiques déterministes, les SDA parallélisables apparaissent comme un cas particulier des SDA du type gradient. Les résultats obtenus généralisent des théorèmes bien connus dans le cadre déterministe.
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