Random perturbations of non-uniformly expanding maps

Details Random perturbations of non-uniformly expanding maps Random perturbations of non-uniformly expanding maps

2000-11-21

arxiv.org/abs/math/0011158v1

Asterisque 286, 25-62 (2003)

Mathematics

Dynamical Systems

44 pages, 2 figures

Scientific paper

We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical asymptotic behaviour of random orbits is bounded by the number of SRB measures if the noise level is small enough. As an application of these results we prove the stochastic stability of certain classes of non-uniformly expanding maps introduced in \cite{V} and \cite{ABV}.

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