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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Moduli of continuity for the Lyapunov exponents of random $\mathrm {GL}(2)$-cocycles


Authors: El Hadji Yaya Tall and Marcelo Viana
Journal: Trans. Amer. Math. Soc. 373 (2020), 1343-1383
MSC (2010): Primary 34D08; Secondary 37H15
DOI: https://doi.org/10.1090/tran/7973
Published electronically: October 24, 2019
MathSciNet review: 4068266
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Abstract | References | Similar Articles | Additional Information

Abstract: The Lyapunov exponents of i.i.d. random $\mathrm {GL}(2)$-cocycles are Hölder continuous functions of the underlying probability distribution at each point with a simple Lyapunov spectrum. Moreover, they are log-Hölder continuous at every point.


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Additional Information

El Hadji Yaya Tall
Affiliation: IMPA, Est. Dona Castorina 110, Jardim Botânico, 22460-320 Rio de Janeiro, Brazil
ORCID: [object Object]
Email: elhadji@impa.br

Marcelo Viana
Affiliation: IMPA, Est. Dona Castorina 110, Jardim Botânico, 22460-320 Rio de Janeiro, Brazil
MR Author ID: 178260
ORCID: 0000-0001-8344-7251
Email: viana@impa.br

Received by editor(s): June 22, 2018
Received by editor(s) in revised form: August 3, 2019
Published electronically: October 24, 2019
Additional Notes: This work was partially supported by Fondation Louis D.—Institut de France (project coordinated by the second author), CNPq, and FAPERJ
Article copyright: © Copyright 2019 American Mathematical Society