Unique equilibrium states for Bonatti-Viana diffeomorphisms

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.

46 pages, 2 figures. In response to referee reports, we added an appendix on the regularity of the geometric potential, and made other suggested minor changes. Accepted for publication in Nonlinearity

References in corpus (2)

• Thermodynamics of Towers of Hyperbolic Type
• Thermodynamics of the Katok Map

Cited by in corpus (2)

• Unique equilibrium states for flows and homeomorphisms with non-uniform structure
• Equilibrium states for Mañé diffeomorphisms