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May  2006, 15(2): 433-446. doi: 10.3934/dcds.2006.15.433

Hyperbolic sets with nonempty interior

Todd Fisher 1,

1. 

Department of Mathematics, University of Maryland, College Park, MD 20742-4015, United States

Received  October 2004 Revised  November 2005 Published  March 2006

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.
Keywords: Anosov., Dynamical systems, interior, hyperbolic set.
Mathematics Subject Classification: Primary: 37D20, 37D05; Secondary: 37B35, 37C7.
Citation: Todd Fisher. Hyperbolic sets with nonempty interior. Discrete & Continuous Dynamical Systems, 2006, 15 (2) : 433-446. doi: 10.3934/dcds.2006.15.433
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