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Journal of the American Mathematical Society

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Density of positive Lyapunov exponents for $ \mathrm{SL}(2,\mathbb{R})$-cocycles


Author: Artur Avila
Journal: J. Amer. Math. Soc. 24 (2011), 999-1014
MSC (2010): Primary 37H15
DOI: https://doi.org/10.1090/S0894-0347-2011-00702-9
Published electronically: April 8, 2011
MathSciNet review: 2813336
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Abstract: We show that $ \mathrm{SL}(2,\mathbb{R})$-cocycles with a positive Lyapunov exponent are dense in all regularity classes and for all non-periodic dynamical systems. For Schrödinger cocycles, we show prevalence of potentials for which the Lyapunov exponent is positive for a dense set of energies.


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Additional Information

Artur Avila
Affiliation: Institut de Mathématiques de Jussieu, CNRS UMR 7586, 175 rue du Chevaleret, 75013, Paris, France; IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil
Email: artur@math.sunysb.edu

DOI: https://doi.org/10.1090/S0894-0347-2011-00702-9
Received by editor(s): May 25, 2010
Received by editor(s) in revised form: August 2, 2010, and March 22, 2011
Published electronically: April 8, 2011
Additional Notes: This research was partially conducted during the period when the author was a Clay Research Fellow
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.