Equilibrium states for Mañé diffeomorphisms
arXiv:1703.05722
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 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.
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 Mañé 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 Mañé class. 28 pages, 1 figure