Journal of Modern Dynamics (JMD)

Bernoulli equilibrium states for surface diffeomorphisms

Pages: 593 - 608, Issue 3, July 2011      doi:10.3934/jmd.2011.5.593

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Omri M. Sarig - Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot, Israel (email)

Abstract: Suppose $f\colon M\to M$ is a $C^{1+\alpha}$ $(\alpha>0)$ diffeomorphism on a compact smooth orientable manifold $M$ of dimension 2, and let $\mu_\Psi$ be an equilibrium measure for a Hölder-continuous potential $\Psi\colon M\to \mathbb R$. We show that if $\mu_\Psi$ has positive measure-theoretic entropy, then $f$ is measure-theoretically isomorphic mod $\mu_\Psi$ to the product of a Bernoulli scheme and a finite rotation.

Keywords:  Bernoulli, surface diffeomorphisms, equilibrium measures, countable Markov partitions.
Mathematics Subject Classification:  Primary: 37D35; Secondary: 37D25.

Received: May 2011;      Revised: July 2011;      Available Online: November 2011.