English

Physical measures at the boundary of hyperbolic maps

Dynamical Systems 2008-05-24 v3

Abstract

We consider diffeomorphisms of a compact manifold with a dominated splitting which is hyperbolic except for a "small" subset of points (Hausdorff dimension smaller than one, e.g. a denumerable subset) and prove the existence of physical measures and their stochastical stability. The physical measures are obtained as zero-noise limits which are shown to satisfy the Entropy Formula.

Keywords

Cite

@article{arxiv.math/0409391,
  title  = {Physical measures at the boundary of hyperbolic maps},
  author = {Vitor Araujo and Ali Tahzibi},
  journal= {arXiv preprint arXiv:math/0409391},
  year   = {2008}
}

Comments

29 pages, 2 figures, 44 references. Minor corrections

R2 v1 2026-07-22T17:10:03.822Z