Log H\'older continuity of the rotation number

Autor:	Gorodetski, Anton, Kleptsyn, Victor
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Spectral Theory 37E45 37E10 81Q10
Druh dokumentu:	Working Paper
Popis:	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. Comment: 10 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.15462 Zobrazit plný text záznamu View this record from Arxiv