JMD
Bernoulli equilibrium states for surface diffeomorphisms
Omri M. Sarig
Journal of Modern Dynamics 2011, 5(3): 593-608 doi: 10.3934/jmd.2011.5.593
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

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