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Equilibrium states for Mañé diffeomorphisms

Published online by Cambridge University Press:  18 January 2018

VAUGHN CLIMENHAGA ,
TODD FISHER  and
DANIEL J. THOMPSON
VAUGHN CLIMENHAGA
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204, USA email [email protected]
TODD FISHER
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA email [email protected]
DANIEL J. THOMPSON
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA email [email protected]
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Abstract

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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 9 , September 2019 , pp. 2433 - 2455
Copyright
© Cambridge University Press, 2018 

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