Equilibrium states for Ma\~n\'e diffeomorphisms

Abstract

We study thermodynamic formalism for the family of robustly transitive diffeomorphisms introduced by Ma\~n\'e, establishing existence and uniqueness of equilibrium states for natural classes of potential functions. In particular, we characterize the SRB 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.