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Hyperbolic sets with nonempty interior

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


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