Reducibility or nonuniform hyperbolicity for quasiperiodic Schrodinger cocycles

• 成果类型: Article
• 署名作者: Avila, Artur; Krikorian, Raphael
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.164.911
• 发表日期: 2006
• 页码: 911-940
• 关键词: absolutely continuous-spectrum; mathieu operator; integrated density; continuity; potentials; exponents; EQUATIONS; DYNAMICS; matrices; STATES

摘要

We show that for almost every frequency alpha epsilon R\Q, for every C-omega potential nu: R/Z -> 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.