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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Density of positive Lyapunov exponents for $\mathrm {SL}(2,\mathbb {R})$-cocycles
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by Artur Avila PDF
J. Amer. Math. Soc. 24 (2011), 999-1014 Request permission

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 MathĂ©matiques 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
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 24 (2011), 999-1014
  • MSC (2010): Primary 37H15
  • DOI: https://doi.org/10.1090/S0894-0347-2011-00702-9
  • MathSciNet review: 2813336