Sinai-Ruelle-Bowen Measures for Random Dynamical Systems

 

Abstract

In this talk we first give a brief introduction to the set-up of random dynamical systems (RDS). Then we present the notions of invariant measures, entropy, Lyapunov exponents, invariant manifolds. SRB measures are a class of physically relevant invariant measures, characterized by having smooth conditional measures on the unstable manifolds. Results discussed in the talk include: An entropy formula of Pesin type holds true if and only if the invariant measure is SRB (generalizing a well-known result of Ledrappier and Young), SRB measures arising from random perturbations of hyperbolic attractors have nice statistical properties (sample-wise central limit theorem, large deviations etc.). Possible extensions to global attractors of infinite-dimensional dynamical systems will be proposed.