The Ten Martini Problem

2005/03/17 by Artur Avila, Svetlana Jitomirskaya · 1 citation
Mathematics · Physics and Astronomy · #math.DS #math-ph #math.MP #math.SP

paper · pdf · doi:10.1007/3-540-34273-7_2

31 pages, no figures

arxiv created 2005/03/17 · arxiv updated 2015/06/26

Abstract

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 non-zero values of the coupling and all irrational frequencies.

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