Anosov Endomorphisms on surfaces: regularity of foliations and rigidity
Marisa do Reis Cantarino (UFF)

We introduce with examples the uniformly hyperbolic dynamics for the non-invertible case and its main properties. We present (in collaboration with R. Varão) a result that characterizes on surfaces the smooth conjugacy between a special Anosov endomorphism and its linearization in terms of the regularity of stable and unstable foliations. This regularity is absolute continuity in a uniformly bounded formulation, which we characterize (in collaboration with R. Varão and S. Targino) using holonomies.