具有奇异点的解析拟周期余圈与扩展Harper模型的李雅普诺夫指数
Analytic quasi-perodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model
摘要：
我们展示了如何扩展（以及有什么限制）阿维拉的全球理论分析SL（2，C）cocycles家庭的cocycles与奇点。这使我们能够开发一种策略，以确定扩展的哈珀模型的李雅普诺夫指数，所有的参数值和所有的无理频率。特别是，这包括自对偶制度，甚至启发式的结果以前不存在于物理学文献。Avila的整体理论的扩展也表明，意味着连续行为的LE上的解析$M_2(\mathbb{C})$ -上循环的空间。这包括迄今尚未得到的频率的合理近似值。
英文摘要：
We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic $M_2(\mathbb{C})$-cocycles. This includes rational approximation of the frequency, which so far has not been available.
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