Unique Equilibrium States for the Robustly Transitive Diffeomorphisms of Mañé and Bonatti–viana

We show that the families of robustly transitive diffeomorphisms of Mañé and Bonatti–Viana have unique equilibrium states for natural classes of potentials. In particular, for any Hölder continuous potential on the phase space of one of these families, we construct a C-open neighborhood of a diffeomorphism in that family for which the potential has a unique equilibrium state. We also characterize the SRB measures for these diffeomorphisms as unique equilibrium states for a suitable geometric potential. These results are an application of general machinery developed by the first and last named authors, and are among the first results on uniqueness of equilibrium states in the setting of diffeomorphisms with partial hyperbolicity or dominated splittings.