2024/10/20 by Gorodetski, Anton, Kleptsyn, Victor
#37E10 #37E45 #81Q10 #Dynamical Systems (math.DS) #FOS: Mathematics #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2410.15462
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-Hölder 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 Schrödinger operator must be log-Hölder.