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Equilibrium states for Mañé diffeomorphisms

Published online by Cambridge University Press:  18 January 2018

VAUGHN CLIMENHAGA
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204, USA email climenha@math.uh.edu
TODD FISHER
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA email tfisher@mathematics.byu.edu
DANIEL J. THOMPSON
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA email thompson@math.osu.edu

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
Copyright
© Cambridge University Press, 2018 

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