C^k-Robust transitivity for surfaces with boundary

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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.
16 pages, 3 figures

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Dynamical Systems, 37E30; 37G25; 37D50

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http://salesiana.dossiersoluciones.com/handle/123456789/227389

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0904.2561
 http://arxiv.org/abs/0904.2561

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arXiv