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

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Abstract

Let AC D (M,SL(d,ℝ)) denote the pairs (f,A) so that f ∈ A ⊂ 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)).

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Authors and Affiliations

  1. Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d’ Ávila e Bolama, 6201-001, Covilhã, Portugal

    Mário Bessa

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

    Paulo Varandas

Authors
  1. Mário Bessa
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  2. Paulo Varandas
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Correspondence to Mário Bessa.

Additional information

Supported by FCT-Fundação para a Ciência e a Tecnologia and CNPq-Brazil (Grant No. PEst-OE/MAT/UI0212/2011)

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Bessa, M., Varandas, P. Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics. Acta. Math. Sin.-English Ser. 31, 1113–1122 (2015). https://doi.org/10.1007/s10114-015-4417-z

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  • DOI: https://doi.org/10.1007/s10114-015-4417-z

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