Stochastic stability of non-uniformly hyperbolic diffeomorphisms

José F. Alves, Vítor Araújo, CARLOS VASQUEZ EHRENFELD

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9 Scopus citations

Abstract

We prove that the statistical properties of random perturbations of a diffeomorphism with dominated splitting having mostly contracting center-stable direction and non-uniformly expanding center-unstable direction 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 C 2 -open class of non-uniformly hyperbolic diffeomorphisms introduced by Alves, Bonatti and Viana in [2] are stochastically stable.

Original languageEnglish
Pages (from-to)299-333
Number of pages35
JournalStochastics and Dynamics
Volume7
Issue number3
DOIs
StatePublished - 1 Sep 2007

Keywords

  • Dominated splitting
  • Non-uniform hyperbolicity
  • Random perturbation
  • SRB measure
  • Stochastic stability

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