Reducibility or nonuniform hyperbolicity for quasiperiodic Schrodinger cocycles

被引:129
作者
Avila, Artur [1 ]
Krikorian, Raphael [1 ]
机构
[1] Coll France, F-75231 Paris, France
基金
加拿大自然科学与工程研究理事会;
关键词
D O I
10.4007/annals.2006.164.911
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
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.
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页码:911 / 940
页数:30
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