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Expansive homeomorphisms and hyperbolic diffeomorphisms on 3-manifolds

Published online by Cambridge University Press:  19 September 2008

José L. Vieitez
José L. Vieitez
Affiliation:
Inst. de Matemática, Fac. de Ingenieria, Universidad de la República, Montevideo, Uruguay
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Abstract

This paper is a contribution to the classification problem of expansive homeomorphisms. Let M be a compact connected oriented three dimensional topological manifold without boundary and f: M → M an expansive homeomorphism.We show that if the topologically hyperbolic period points of f are dense in M then M = , and f is conjugate to an Anosov diffeomorphism. This follows from our basic result: for such a homeomorphism, all stable and unstable sets are (tamely embedded) topological manifolds.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 3 , June 1996 , pp. 591 - 622
Copyright
Copyright © Cambridge University Press 1996

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