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

Bessa, Mário; Varandas, Paulo

http://hdl.handle.net/10400.2/13898

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Authors

Bessa, Mário

Varandas, Paulo

Abstract(s)

Let AC_D(M,SL(d,R)) denote the pairs (f,A) so that f ∈ A ⊂ Diff (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 Aut_Leb(M) × Lp(M,SL(d,R)).

Keywords

Linear cocycles Lyapunov exponents Anosov diffeomorphisms Topological conjugacy Maximal entropy measures

URI

http://hdl.handle.net/10400.2/13898

Citation

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)