C^k-Robust transitivity for surfaces with boundary

Details C^k-Robust transitivity for surfaces with boundary C^k-Robust transitivity for surfaces with boundary

2009-04-16

arxiv.org/abs/0904.2561v1

Mathematics

Dynamical Systems

16 pages, 3 figures

Scientific paper

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 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 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.

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