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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Pseudo-Anosov maps and continuum theory
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by Alfonso Artigue PDF
Proc. Amer. Math. Soc. 145 (2017), 3047-3056 Request permission

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
  • MR Author ID: 863559
  • Email: artigue@unorte.edu.uy
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 3047-3056
  • MSC (2010): Primary 37B45
  • DOI: https://doi.org/10.1090/proc/13450
  • MathSciNet review: 3637952