Stochastic stability of diffeomorphisms with dominated splitting
Abstract
We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic stability of such dynamical systems. We show that a certain -open class of nonuniformly hyperbolic diffeomorphisms introduced in [Alves, J; Bonatti, C. and Viana, V., SRB measures for partially hyperbolic systems with mostly expanding central direction, Invent. Math., 140 (2000), 351-398] are stochastically stable. Our setting encompasses that of partially hyperbolic diffeomorphisms as well. Moreover, the techniques used enable us to obtain SRB measures in this setting through zero-noise limit measures.
Cite
@article{arxiv.math/0404160,
title = {Stochastic stability of diffeomorphisms with dominated splitting},
author = {Jose F. Alves and Vitor Araujo and Carlos H. Vasquez},
journal= {arXiv preprint arXiv:math/0404160},
year = {2011}
}
Comments
32 pages; introduction revised and proofs detailed