Transitivity and Topological Mixing for \({C}^{1}\) Diffeomorphisms

Chapter

Abstract

We prove that, on connected compact manifolds, both C 1-generic conservative diffeomorphisms and C 1-generic transitive diffeomorphisms are topologically mixing. This is obtained through a description of the periods of a homoclinic class and by a control of the period of the periodic points given by the closing lemma.

Keywords

Periodic Orbit Periodic Point Closing Lemma Homoclinic Class Hyperbolic Periodic Orbit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Ventor InvestimentosRio de JaneiroBrazil
  2. 2.Département de Mathématiques, UMR 8628Université Paris-Sud 11Orsay, CedexFrance

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