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- W4386043536 abstract "We solve the ten martini problem (Cantor spectrum with no condition on irrational frequencies, previously only established for the almost Mathieu) for a large class of one-frequency quasiperiodic operators, including nonperturbative analytic neighborhoods of several popular explicit families. The proof is based on the structural analysis of dual cocycles as introduced in [35]. As a part of the proof, we develop several general ingredients of independent interest: Kotani theory, for a class of finite-range operators over general minimal underlying dynamics, making the first step towards and providing a partial solution of the Kotani-Simon problem, simplicity of point spectrum for the same class, and the all-frequency version of Puig's argument." @default.
- W4386043536 created "2023-08-22" @default.
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- W4386043536 date "2023-08-18" @default.
- W4386043536 modified "2023-09-25" @default.
- W4386043536 title "Kotani theory, Puig's argument, and stability of The Ten Martini Problem" @default.
- W4386043536 doi "https://doi.org/10.48550/arxiv.2308.09321" @default.
- W4386043536 hasPublicationYear "2023" @default.
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