Description:
We prove that C1-robustly transitive diffeomorphisms on surfaces with boundary do not exist, and we exhibit a class of diffeomorphisms of surfaces with boundary which are Ck..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 C2..topology. This follows showing that blowup of pseudo-Anosov diffeomorphisms on surfaces without boundary, become C2..robustly topologically mixing diffeomorphisms on a surfaces with boundary.