Seminar 2.19.15 Thompson

Speaker: Dan Thompson (Ohio State)

Title: Unique equilibrium states for the robustly transitive diffeomorphisms of Mañé and Bonatti-Viana

Abstract: We establish results on uniqueness of equilibrium states for the well-known Mañé and Bonatti-Viana examples of robustly transitive diffeomorphisms. This is an application of machinery developed by Vaughn Climenhaga and myself, which applies when systems satisfy suitably weakened versions of expansivity and the specification property. The Mañé examples are partially hyperbolic, whereas the Bonatti-Viana examples are not partially hyperbolic but admit a dominated splitting. I’ll explain why these maps satisfy our hypotheses. This is joint work with Vaughn Climenhaga (Houston) and Todd Fisher (Brigham Young).