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arXiv · 1509.02591

Pseudo-Anosov maps and continuum theory

Alfonso Artigue
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Abstract

In the hyperspace of subcontinua of a compact surface we consider a second order Hausdorff distance. This metric space is compactified in such a way that the stable foliation of a pseudo-Anosov map is naturally identified with a hypercontinuum. We show that negative iterates of a stable arc converges to this hypercontinuum in the considered metric. Some dynamical properties of pseudo-Anosov maps, as topological mixing and the density of stable leaves, are generalized for cw-expansive homeomorphisms of pseudo-Anosov type on compact metric spaces.

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Alfonso Artigue. 2015-09-09. Pseudo-Anosov maps and continuum theory. https://arxiv.org/abs/1509.02591

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