English

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 C1C^1 topology, to a conjecture of Pugh-Shub in the context of partially hyperbolic conservative diffeomorphisms with two dimensional center bundle.

Keywords

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

R2 v1 2026-06-21T09:30:45.052Z