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Equilibrium states for Mañé diffeomorphisms

Published online by Cambridge University Press:  18 January 2018

Department of Mathematics, University of Houston, Houston, TX 77204, USA email
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA email
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA email


We study thermodynamic formalism for the family of robustly transitive diffeomorphisms introduced by Mañé, establishing existence and uniqueness of equilibrium states for natural classes of potential functions. In particular, we characterize the Sinaĭ–Ruelle–Bowen measures for these diffeomorphisms as unique equilibrium states for a suitable geometric potential. We also obtain large deviations and multifractal results for the unique equilibrium states produced by the main theorem.

Original Article
© Cambridge University Press, 2018 

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