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arXiv · 2410.15462

Log H\"older continuity of the rotation number

Anton Gorodetski·Victor Kleptsyn
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Abstract

We consider one-parameter families of smooth circle cocycles over an ergodic transformation in the base, and show that their rotation numbers must be log-H\"older regular with respect to the parameter. As an immediate application, we get a dynamical proof of 1D version of the Craig-Simon theorem that establishes that the integrated density of states of an ergodic Schr\"odinger operator must be log-H\"older.

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Anton Gorodetski, Victor Kleptsyn. 2024-10-20. Log H\"older continuity of the rotation number. https://arxiv.org/abs/2410.15462

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