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Pseudo-Anosov maps and continuum theory

Author: Alfonso Artigue
Journal: Proc. Amer. Math. Soc. 145 (2017), 3047-3056
MSC (2010): Primary 37B45
Published electronically: January 25, 2017
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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 converge 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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Additional Information

Alfonso Artigue
Affiliation: Departamento de Matemática y Estadistica del Litoral, Universidad de la República, Gral. Rivera 1350, 50000 Salto, Uruguay

Received by editor(s): August 2, 2015
Received by editor(s) in revised form: June 13, 2016, and August 25, 2016
Published electronically: January 25, 2017
Communicated by: Nimish Shah
Article copyright: © Copyright 2017 American Mathematical Society

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