Topological obstruction for robustly transitive endomorphisms on surfaces.

We give necessary conditions for the existence of robustly transitive maps on surfaces. We nd topological obstructions that determine which surfaces support robustly transitive endomorphisms. Concretely, dominated splitting is a necessary condition in order to have C1 robustly transitive endomorphisms with critical points on surfaces, and if a surface support a robustly transitive map, then it is the Torus or the Klein bottle. In particular, there not exist robustly transitive maps on the 2-sphere. Moreover,
every robustly transitive endomorphism is homotopic to a linear map having at least one eigenvalue with modulus larger than one.

This is a joint work with Wagner Ranter (UFAL).