Random perturbations of non-uniformly expanding maps
Dynamical Systems
2010-07-20 v1
Abstract
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}.
Cite
@article{arxiv.math/0011158,
title = {Random perturbations of non-uniformly expanding maps},
author = {Jose F. Alves and Vitor Araujo},
journal= {arXiv preprint arXiv:math/0011158},
year = {2010}
}
Comments
44 pages, 2 figures