Kotani 理论、Puig 论证与十马提尼问题的稳定性
Kotani theory, Puig's argument, and stability of The Ten Martini Problem
AI总结：
本文利用对偶上循环结构分析，将十马提尼问题推广到一大类单频准周期算子，并建立 Kotani 理论、点谱简单性及全频率 Puig 论证等独立结果。
摘要：
我们针对一大类单频准周期算子解决了十马提尼问题（即 Cantor 谱，且对无理频率不加任何条件；此前该结论仅对 almost Mathieu 算子确立），其中包括若干常用显式族的非微扰解析邻域。证明基于文献 [35] 所引入的对偶上循环的结构分析。作为证明的一部分，我们发展了若干具有独立意义的一般性要素：适用于一般极小底层动力系统上一类有限程算子的 Kotani 理论，这为 Kotani–Simon 问题迈出第一步并给出部分解答；同一类算子点谱的简单性；以及 Puig 论证的全频率版本。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
