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Ergodic Theory and Dynamical Systems Ergodic Theory and Dynamical Systems

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

Part of: Dynamical systems with hyperbolic behavior Random dynamical systems

Published online by Cambridge University Press:  11 April 2019

LUCAS BACKES ,
MAURICIO POLETTI ,
PAULO VARANDAS  and
YURI LIMA
LUCAS BACKES
Affiliation:
Departamento de Matemática, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, CEP 91509-900, Porto Alegre, RS, Brazil email lhbackes@impa.br
MAURICIO POLETTI
Affiliation:
CNRS-Laboratoire de Mathématiques d’Orsay, UMR 8628, Université Paris-Sud 11, Orsay Cedex91405, France email mpoletti@impa.br
PAULO VARANDAS
Affiliation:
Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, CEP 40170-110Salvador, BA, Brazil email paulo.varandas@ufba.br
YURI LIMA
Affiliation:
Departamento de Matemática, Centro de Ciências, Campus do Pici, Universidade Federal do Ceará (UFC), Fortaleza – CE, CEP 60455-760, Brazil email yurilima@gmail.com
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Abstract

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.

Keywords

Lyapunov exponentsnon-uniform hyperbolicitylinear cocyles

MSC classification

Primary: 37H15: Multiplicative ergodic theory, Lyapunov exponents 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
Secondary: 37D30: Partially hyperbolic systems and dominated splittings
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 11 , November 2020 , pp. 2947 - 2969
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Copyright
© Cambridge University Press, 2019

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