Trivial and Simple Spectrum for SL(d,R) Cocycles with Free Base and Fiber Dynamics  

作　　者：Mrio BESSA Paulo VARANDAS 

机构地区：[1]Departamento de Matemtica,Universidade da Beira Interior,Rua Marquês d'vila e Bolama,6201-001 Covilh,Portugal [2]Departamento de Matemtica,Universidade Federal da Bahia,Av.Ademar de Barros s/n,40170-110 Salvador,Brazil

出　　处：《Acta Mathematica Sinica,English Series》2015年第7期1113-1122,共10页数学学报（英文版）

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

摘　　要：Let ACD（M, SL（d,R）） denote the pairs （f, A） so that f∈ A C Diff^1（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 ACD（M, SL（d,R））, in appropriate topologies, the pair （f,A） has simple spectrum with respect to the unique maximal entropy measure μf. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AUtLeb（M） × LP（M, SL（d, R））.Let ACD（M, SL（d,R）） denote the pairs （f, A） so that f∈ A C Diff^1（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 ACD（M, SL（d,R））, in appropriate topologies, the pair （f,A） has simple spectrum with respect to the unique maximal entropy measure μf. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AUtLeb（M） × LP（M, SL（d, R））.

关 键 词：Linear cocycles Lyapunov exponents Anosov diffeomorphisms topological conjugacy maximal entropy measures 

分 类 号：O186.12[理学—数学]