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Acta Mathematica Sinica, English Series

, Volume 31, Issue 7, pp 1113–1122 | Cite as

Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics

  • Mário Bessa
  • Paulo Varandas
Article
  • 55 Downloads

Abstract

Let AC D (M,SL(d,ℝ)) denote the pairs (f,A) so that fA ⊂ Diff1(M) is a C 1-Anosov transitive diffeomorphisms and A is an SL(d,ℝ) cocycle dominated with respect to f. We prove that open and densely in AC D (M,SL(d,ℝ)), in appropriate topologies, the pair (f,A) has simple spectrum with respect to the unique maximal entropy measure µ f . Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AutLeb(M) × L p (M,SL(d,ℝ)).

Keywords

Linear cocycles Lyapunov exponents Anosov diffeomorphisms topological conjugacy maximal entropy measures 

MR(2010) Subject Classification

37A20 37D25 37F15 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade da Beira InteriorCovilhãPortugal
  2. 2.Departamento de MatemáticaUniversidade Federal da BahiaSalvadorBrazil

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