The Ten Martini Problem

被引：226

作者：

Avila, Artur ^{[1
,2
]}

Jitomirskaya, Svetlana ^{[3
]}

机构：

[1] Univ Paris 06, CNRS, UMR 7599, Lab Probabilites & Modeles Aleatoires, F-75252 Paris 05, France

[2] IMPA, BR-22460320 Rio De Janeiro, Brazil

[3] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

ANNALS OF MATHEMATICS | 2009年 / 170卷 / 01期

关键词：

QUASI-PERIODIC OPERATORS; MATHIEU OPERATOR; CANTOR SPECTRUM; LOCALIZATION; CONTINUITY; POTENTIALS; THEOREM;

D O I：

10.4007/annals.2009.170.303

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the conjecture (known as the "Ten Martini Problem" after Kac and Simon) that the spectrum of the almost Mathieu operator is a Cantor set for all nonzero values of the coupling and all irrational frequencies.

引用

页码：303 / 342

页数：40

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