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.