V. Climenhaga, T. Fisher, D. J. Thompson
Published 2017-03-16Version 1
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.
Comments: This work develops material that originally appeared in the first version of arxiv:1505.06371, originally titled 'Unique equilibrium states for the robustly transitive diffeomorphisms of Ma\~n\'e and Bonatti-Viana'. We split this material into two papers: arxiv:1505.06371 now treats the Bonatti-Viana class and general estimates; this article studies the Ma\~n\'e class. 27 pages, 1 figure
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