# American Institute of Mathematical Sciences

April  2011, 30(1): 1-16. doi: 10.3934/dcds.2011.30.1

## Recurrence for random dynamical systems

 1 Université d'Aix-Marseille, Centre de physique théorique, UMR 6206 CNRS, Campus de Luminy, Case 907, 13288 Marseille cedex 9 and Université du Sud, Toulon-Var, France 2 Université Européenne de Bretagne, Université de Brest, Laboratoire de Mathématiques CNRS UMR 6205,6 avenue Victor le Gorgeu, CS93837, F-29238 Brest Cedex 3, France

Received  December 2009 Revised  May 2010 Published  February 2011

This paper is a first step in the study of the recurrence behaviour in random dynamical systems and randomly perturbed dynamical systems. In particular we define a concept of quenched and annealed return times for systems generated by the composition of random maps. We moreover prove that for super-polynomially mixing systems, the random recurrence rate is equal to the local dimension of the stationary measure.
Citation: Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1
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