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1 results

  • log-Hölder continuity of the rotation number

  • Part of
  • ANTON GORODETSKI, VICTOR KLEPTSYN
  • Journal:
    Ergodic Theory and Dynamical Systems , First View
    Published online by Cambridge University Press:
    08 July 2025, pp. 1-11
    • Article
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  • 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 the one-dimensional version of the Craig–Simon theorem that establishes that the integrated density of states of an ergodic Schrödinger operator must be log-Hölder.