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

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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Veröffentlicht in:Ergodic theory and dynamical systems 2020-11, Vol.40 (11), p.2947-2969
Hauptverfasser: BACKES, LUCAS, POLETTI, MAURICIO, VARANDAS, PAULO, LIMA, YURI
Format: Artikel
Sprache:eng
Schlagworte:
Continuous fibers
Hyperbolic systems
Original Article
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Zusammenfassung: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2019.22