English

Reducibility or non-uniform hyperbolicity for quasiperiodic Schrodinger cocycles

Dynamical Systems 2007-05-23 v3 Mathematical Physics math.MP Spectral Theory

Abstract

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 Schrodinger 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 Schrodinger operator, and allows us to complete the proof of the Aubry-Andre conjecture on the measure of the spectrum of the Almost Mathieu Operator.

Keywords

Cite

@article{arxiv.math/0306382,
  title  = {Reducibility or non-uniform hyperbolicity for quasiperiodic Schrodinger cocycles},
  author = {Artur Avila and Raphael Krikorian},
  journal= {arXiv preprint arXiv:math/0306382},
  year   = {2007}
}

Comments

30 pages, published version

R2 v1 2026-07-22T16:55:44.593Z