Hyperbolic sets with nonempty interior

Todd Fisher

doi:10.3934/dcds.2006.15.433

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2006, Volume 15, Issue 2: 433-446. Doi: 10.3934/dcds.2006.15.433

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Hyperbolic sets with nonempty interior

Todd Fisher^1,

1.
Department of Mathematics, University of Maryland, College Park, MD 20742-4015

Received: September 30, 2004

Revised: October 31, 2005

Published: March 2006

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Abstract

In this paper we study hyperbolic sets with nonempty interior. We prove the folklore theorem that every transitive hyperbolic set with interior is Anosov. We also show that on a compact surface every locally maximal hyperbolic set with nonempty interior is Anosov. Finally, we give examples of hyperbolic sets with nonempty interior for a non-Anosov diffeomorphism.

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Mathematics Subject Classification: Primary: 37D20, 37D05; Secondary: 37B35, 37C70.

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