N-expansive homeomorphisms on surfaces-Reference-Cited by-同舟云学术

N-expansive homeomorphisms on surfaces

Published:2016-11-24 Issue:01 Volume:19 Page:1650040
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Artigue A.¹,Pacifico M. J.²,Vieitez J. L.¹

Affiliation:

1. Regional Norte, Universidad de la República, Rivera 1350, CP 50000, Salto, Uruguay

2. Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil

Abstract

In this paper, we study [Formula: see text]-expansive homeomorphisms on surfaces. We prove that when [Formula: see text] is a [Formula: see text]-expansive homeomorphism defined on a compact boundaryless surface [Formula: see text] with non-wandering set [Formula: see text] being the whole of [Formula: see text] then [Formula: see text] is expansive. This condition on the non-wandering set cannot be relaxed: we present an example of a [Formula: see text]-expansive homeomorphisms on a surface with genus [Formula: see text] with wandering points that is not expansive.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199716500401

Reference19 articles.

1. Entropy-expansive maps

2. Expansive Self-Homeomorphisms of a Compact Metric Space

3. Expansiveness, hyperbolicity and Hausdorff dimension

4. Anosov diffeomorphisms

5. A quasi-Anosov diffeomorphism that is not Anosov

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