Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems

We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a $u$-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched linear cocycles.

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 40; no. 11; pp. 2947 - 2969
Main Authors BACKES, LUCAS, POLETTI, MAURICIO, VARANDAS, PAULO, LIMA, YURI
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.11.2020
Subjects
Continuous fibers
Hyperbolic systems
Original Article
37H15
linear cocyles
37D25
Lyapunov exponents
non-uniform hyperbolicity
37D30
Online AccessGet full text
ISSN0143-3857
1469-4417
DOI10.1017/etds.2019.22

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Summary:We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a $u$-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched linear cocycles.
Bibliography:ObjectType-Article-1
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ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2019.22