Đề tài " Reducibility or nonuniform hyperbolicity for quasiperiodic Schr¨odinger cocycles "

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