Unique equilibrium states for Bonatti-Viana diffeomorphisms

TL;DR

This paper proves that certain robustly transitive diffeomorphisms, including Bonatti-Viana examples, have unique equilibrium states for natural potentials, with SRB measures characterized as such, and these results are stable under small perturbations.

Contribution

It establishes the uniqueness of equilibrium states for a broad class of DA diffeomorphisms, extending previous results to include Bonatti-Viana examples and their perturbations.

Findings

Unique equilibrium states for Bonatti-Viana diffeomorphisms

SRB measure characterized as a unique equilibrium state

Results stable under $C^1$ perturbations

Abstract

We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potentials. In particular, we characterize the SRB measure as the unique equilibrium state for a suitable geometric potential. The techniques developed are applicable to a wide class of DA diffeomorphisms, and persist under $C^1$ perturbations of the map. These results are an application of general machinery developed by the first and last named authors.