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

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 th...

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Bibliographic Details
Published in:数学学报：英文版 2015 (7), p.1113-1122
Main Author: Mario BESSA Paulo VARANDAS
Format: Article
Language:English
Subjects:
ACD
光纤
差速器
微分同胚
拓扑结构
游离碱
熵测度
证明
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Summary: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））.
ISSN:1439-8516
1439-7617