It is known that the Lyapunov exponent for multifrequency analytic cocycles is weak-Hölder continuous in cocycle for certain Diophantine frequencies, and that this implies certain regularity of the integrated density of states in energy for Jacobi operators. In this paper, we establish the pointwise modulus of continuity in both cocycle and frequency and obtain analogous regularity of the integrated density of states in energy, potential, and frequency.

中文翻译：

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解析多频准周期 M(2,C) 余循环的 Lyapunov 指数的逐点连续模量和积分态密度

众所周知，对于某些丢番图频率，多频解析余循环的李亚普诺夫指数在余循环中是弱霍尔德连续的，这意味着雅可比算子的能量积分状态密度具有一定的规律性。在本文中，我们建立了余循环和频率的逐点连续性模量，并获得了能量、势能和频率的积分态密度的类似规律。