Preprint A625/2009
C^k -Robust Transitivity for Surfaces with Boundary
Enrique R. Pujals | Arroyo, Aubin
Keywords: Robust transitivity | Blow-up of Pseudo-Anosov Maps | Diffeomorphisms of Surfaces.
We prove that C^1 robustly transitive diffeomorphisms on surfaces with boundary do not exist, and we exhibit a class of diffeomorphisms of surfaces with boundary which are C^k robustly transitive, with k >= 2. This class of diffeomorphisms are examples where a version of Palis conjecture on surfaces with boundary, about homoclinic tangencies and uniform hyperbolicity, does not hold in the C^2 topology. This follows showing that blow- up of pseudo Anosov diffeomorphisms on surfaces without boundary, become C^2 robustly topologically mixing diffeomorphisms on a surfaces with boundary.