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New criteria for hyperbolicity based on periodic sets

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Abstract

We prove some criteria for uniform hyperbolicity based on the periodic points of the transformation. More precisely, if a mild hyperbolicity condition holds for the periodic points of any diffeomorphism in a residual subset of a C 1-open set U then there exists an open and dense subset A ⊂ U of Axiom A diffeomorphisms. Moreover, we also prove a noninvertible version of Ergodic Closing Lemma which we use to prove a counterpart of this result for local diffeomorphisms.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110, Salvador, BA, Brazil

    Armando Castro

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  1. Armando Castro
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Correspondence to Armando Castro.

Additional information

Work carried out at the Federal University of Bahia. Partially supported by CNPq (PQ 10/2007) and UFBA.

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Castro, A. New criteria for hyperbolicity based on periodic sets. Bull Braz Math Soc, New Series 42, 455–483 (2011). https://doi.org/10.1007/s00574-011-0025-4

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  • DOI: https://doi.org/10.1007/s00574-011-0025-4

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