The Ten Martini Problem

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 nonzero values of the coupling and all irrational frequencies.

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    @article{AK, MRKEY = {2259248},
      AUTHOR = {Avila, Artur and Krikorian, Rapha{ë}l},
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    @techreport{AK2,
      author = {Avila, A. and Krikorian, R.},
      TITLE = {Quasiperiodic {$\operatorname{SL}(2,\mathbb{R})$} cocycles},
      TYPE = {in preparation},
      marginpar = {please supply any updates},
      }
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Authors

Artur Avila

IMPA
Estrada Dona Castorina 110
Jardim Botânico
22460-320 Rio de Janeiro, RJ
Brazil

Svetlana Jitomirskaya

Department of Mathematics
340 Rowland Hall
University of California
Irvine, CA 92697-3875
United States