Log H\"older continuity of the rotation number
Dynamical Systems
2024-10-22 v1 Spectral Theory
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.
Cite
@article{arxiv.2410.15462,
title = {Log H\"older continuity of the rotation number},
author = {Anton Gorodetski and Victor Kleptsyn},
journal= {arXiv preprint arXiv:2410.15462},
year = {2024}
}
Comments
10 pages