A Criterion For Ergodicity of Non-uniformly hyperbolic Diffeomorphisms

Details A Criterion For Ergodicity of Non-uniformly hyperbolic Diffeomorphisms A Criterion For Ergodicity of Non-uniformly hyperbolic Diffeomorphisms

2007-10-11

arxiv.org/abs/0710.2353v1

Mathematics

Dynamical Systems

A Research Announcement

Scientific paper

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

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