Smooth Ergodic Theory of Random Dynamical Systems

Pei-Dong Liu, Min Qian (auth.)3540600043, 9783540600046, 0387600043

This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer’s book. An entropy formula of Pesin’s type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

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Table of contents :
Preliminaries….Pages 1-21
Entropy and Lyapunov exponents of random diffeomorphisms….Pages 22-44
Estimation of entropy from above through Lyapunov exponents….Pages 45-54
Stable invariant manifolds of random diffeomorphisms….Pages 55-90
Estimation of entropy from below through Lyapunov exponents….Pages 91-108
Stochastic flows of diffeomorphisms….Pages 109-127
Characterization of measures satisfying entropy formula….Pages 128-181
Random perturbations of hyperbolic attractors….Pages 182-206