A Criterion For Ergodicity of Non-uniformly hyperbolic Diffeomorphisms

2007/10/11 by Federico Rodriguez Hertz, Hertz, F. Rodriguez, M. A. Rodriguez Hertz +5 · 1 citation
Mathematics · Physics and Astronomy · #37D30 #37D35 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.0710.2353

openalex publication_date 2007/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 C¹ topology, to a conjecture of Pugh-Shub in the context of partially hyperbolic conservative diffeomorphisms with two dimensional center bundle.

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• Uniqueness of the measure of maximal entropy for geodesic flows on surfaces

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