Hyperbolic sets with nonempty interior

Pages: 433 - 446, Volume 15, Issue 2, June 2006

doi:10.3934/dcds.2006.15.433       Abstract        Full Text (252.0K)       Related Articles

Todd Fisher - Department of Mathematics, University of Maryland, College Park, MD 20742-4015, United States (email)

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.

Keywords:  Dynamical systems, hyperbolic set, interior, Anosov.
Mathematics Subject Classification:  Primary: 37D20, 37D05; Secondary: 37B35, 37C70.

Received: October 2004;      Revised: November 2005;      Published: March 2006.