Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles

• Autores: Raffi Krikorian, Artur Avila
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 164, Nº 3, 2006, págs. 911-940
• Idioma: inglés
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• Resumen

  • We show that for almost every frequency ¿¿ ¿¿ R\Q, for every C¿Ö potential v : R/Z ¿¿ R, and for almost every energy E the corresponding quasiperiodic Schr¿Nodinger cocycle is either reducible or nonuniformly hyperbolic. This result gives very good control on the absolutely continuous part of the spectrum of the corresponding quasiperiodic Schr¿Nodinger operator, and allows us to complete the proof of the Aubry-Andr¿Le conjecture on the measure of the spectrum of the Almost Mathieu Operator.