A Criterion For Ergodicity of Non-uniformly hyperbolic Diffeomorphisms

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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.
A Research Announcement

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Dynamical Systems, 37D30, 37D35

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http://salesiana.dossiersoluciones.com/handle/123456789/139901

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.2353
 http://arxiv.org/abs/0710.2353

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arXiv