Continuity of Lyapunov exponents for cocycles with invariant holonomies

Lucas Backes; Aaron Brown; Clark Butler

doi:10.3934/jmd.2018009

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2018, Volume 12: 223-260. Doi: 10.3934/jmd.2018009

This volume Previous Article Countable Markov partitions suitable for thermodynamic formalism Next Article On the non-equivalence of the Bernoulli and $ K$ properties in dimension four

Continuity of Lyapunov exponents for cocycles with invariant holonomies

1.
Departamento de Matemática, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, CEP 91509-900, Porto Alegre, RS, Brazil
2.
Department of Mathematics, University of Chicago, 5734 S University Ave, Chicago, IL 60637, USA

Received: April 03, 2016

Revised: October 10, 2017

Published: July 2018

CB: Supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1144082.

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Abstract

We prove a conjecture of Viana which states that Lyapunov exponents vary continuously when restricted to $GL(2,\mathbb{R})$-valued cocycles over a subshift of finite type which admit invariant holonomies that depend continuously on the cocycle.

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Mathematics Subject Classification: Primary: 37H15, 37D30; Secondary: 37D25, 37E99.

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