The Ten Martini Problem

• 成果类型: Article
• 署名作者: Avila, Artur; Jitomirskaya, Svetlana
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.303
• 发表日期: 2009
• 页码: 303-342
• 关键词: quasi-periodic operators; mathieu operator; cantor spectrum; localization; continuity; potentials; THEOREM

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.