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July 2011, 5(3): 593-608. doi: 10.3934/jmd.2011.5.593
Bernoulli equilibrium states for surface diffeomorphisms
Omri M. Sarig 1,
Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot, Israel
Received May 2011 Revised July 2011 Published November 2011
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: countable Markov partitions., surface diffeomorphisms, Bernoulli, equilibrium measures.
Mathematics Subject Classification: Primary: 37D35; Secondary: 37D2.
Citation: Omri M. Sarig. Bernoulli equilibrium states for surface diffeomorphisms. Journal of Modern Dynamics, 2011, 5 (3) : 593-608. doi: 10.3934/jmd.2011.5.593
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Omri M. Sarig