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Continuity of Lyapunov exponents for non-uniformly fiber-bunched cocycles

Part of: Dynamical systems with hyperbolic behavior Random dynamical systems

Published online by Cambridge University Press:  02 December 2020

CATALINA FREIJO  and
KARINA MARIN
CATALINA FREIJO
Affiliation:
Departamento de Matemática, Instituto de Ciências Exatas (ICEx), Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil (e-mail: catalinafreijo@gmail.com)
KARINA MARIN*
Affiliation:
Departamento de Matemática, Instituto de Ciências Exatas (ICEx), Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil (e-mail: catalinafreijo@gmail.com)
*
e-mail: kmarin@mat.ufmg.br
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Abstract

We provide conditions that imply the continuity of the Lyapunov exponents for non-uniformly fiber-bunched cocycles in $SL(2,\mathbb {R})$ . The main theorem is an extension of the result of Backes, Brown and Butler and gives a partial answer to a conjecture of Marcelo Viana.

Keywords

Lyapunov exponentslinear cocyclesnon-uniformly fiber-bunched

MSC classification

Primary: 37H15: Multiplicative ergodic theory, Lyapunov exponents
Secondary: 37D30: Partially hyperbolic systems and dominated splittings 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 12 , December 2021 , pp. 3740 - 3767
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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