A Criterion For Ergodicity of Non-uniformly hyperbolic Diffeomorphisms
Dynamical Systems
2007-10-15 v1
Abstract
In this work we exhibit a new criteria for ergodicity of diffeomorphisms involving conditions on Lyapunov exponents and general position of some invariant manifolds. On one hand we derive uniqueness of SRB-measures for transitive surface diffeomorphisms. On the other hand, using recent results on the existence of blenders we give a positive answer, in the topology, to a conjecture of Pugh-Shub in the context of partially hyperbolic conservative diffeomorphisms with two dimensional center bundle.
Cite
@article{arxiv.0710.2353,
title = {A Criterion For Ergodicity of Non-uniformly hyperbolic Diffeomorphisms},
author = {F. Rodriguez Hertz and M. A. Rodriguez Hertz and A. Tahzibi and R. Ures},
journal= {arXiv preprint arXiv:0710.2353},
year = {2007}
}
Comments
A Research Announcement