Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Reducibility or non-uniform hyperbolicity for quasiperiodic Schrödinger cocycles

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Résumé: We show that for almost every frequency $\alpha \in \R \setminus \Q$, for every $C^\omega$ potential $v:\R/\Z \to \R$, and for almost every energy $E$ the corresponding quasiperiodic Schr\"odinger cocycle is either reducible or non-uniformly hyperbolic. This result gives a very good control on the absolutely continuous part of the spectrum of the corresponding quasiperiodic Schr\"odinger operator, and allows us to complete the proof of the Aubry-Andr\'e conjecture on the measure of the spectrum of the Almost Mathieu Operator.