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.
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