Robustly N-expansive surface diffeomorphisms

We give sufficient conditions for a diffeomorphism of a compact surface to be robustly $N$-expansive and cw-expansive in the $C^r$-topology. We give examples on the genus two surface showing that they need not to be Anosov diffeomorphisms. The examples are axiom A diffeomorphisms with tangencies at wandering points.Comment: arXiv admin note: text overlap with arXiv:1409.388

Unique equilibrium states for Bonatti-Viana diffeomorphisms

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.Comment: 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 Nonlinearit