On bi-Lyapunov stable homoclinic classes

  • A. Arbieto
  • B. Carvalho
  • W. Cordeiro
  • D. J. Obata


For a C 1 generic diffeomorphism if a bi-Lyapunov stable homoclinic class is homogeneous then it does not have weak eigenvalues. Using this, we show that such homoclinic classes are hyperbolic if it has one of the following properties: shadowing, specification or limit shadowing.


bi-Lyapunov stability hyperbolic generic properties homoclinic classes shadowing specification 

k]Mathematical subject classification

Primary: 37C20 Secondary: 37D20 


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Copyright information

© Sociedade Brasileira de Matemática 2013

Authors and Affiliations

  • A. Arbieto
    • 1
  • B. Carvalho
    • 1
  • W. Cordeiro
    • 1
  • D. J. Obata
    • 1
  1. 1.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de Janeiro, RJBrazil

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