C^k-Robust transitivity for surfaces with boundary

2009/04/16 by Arroyo, Aubin, Pujals, Enrique R.
#37D50 #37E30 #37G25 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.0904.2561

Abstract

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 C^k-robustly transitive, with k greater or equal than 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 blow-up of pseudo-Anosov diffeomorphisms on surfaces without boundary, become C²-robustly topologically mixing diffeomorphisms on a surfaces with boundary.

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