Positivity of the Top Lyapunov Exponent for Cocycles on Semisimple Lie Groups over Hyperbolic Bases

  • Mário Bessa
  • Jairo Bochi
  • Michel Cambrainha
  • Carlos Matheus
  • Paulo VarandasEmail author
  • Disheng Xu


A theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact classical semisimple Lie group.


Lyapunov exponents Linear cocycles Semisimple Lie groups 



The authors are grateful to the referee for a careful reading of the manuscript and for useful suggestions that helped to improve the presentation of the paper.


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Copyright information

© Sociedade Brasileira de Matemática 2017

Authors and Affiliations

  • Mário Bessa
    • 1
  • Jairo Bochi
    • 2
  • Michel Cambrainha
    • 3
  • Carlos Matheus
    • 4
  • Paulo Varandas
    • 5
    Email author
  • Disheng Xu
    • 6
  1. 1.Departamento de MatemáticaUniversidade da Beira InteriorCovilhãPortugal
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile
  3. 3.Departamento de MatemáticaUniversidade Federal do Estado do Rio de JaneiroRio de JaneiroBrazil
  4. 4.Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539)VilletaneuseFrance
  5. 5.Departamento de MatemáticaUniversidade Federal da BahiaSalvadorBrazil
  6. 6.Université Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Université Paris 06ParisFrance

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