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The rate of convergence for function systems on the circle

Volume 159 / 2020

Tomasz Szarek, Anna Zdunik Colloquium Mathematicum 159 (2020), 77-89 MSC: Primary 60F05, 60J05; Secondary 37A25, 37A50. DOI: 10.4064/cm7650-1-2019 Published online: 10 October 2019


The rate of convergence of the iterates of the Markov operator corresponding to an iterated function system consisting of homeomorphisms of the circle is provided. As an application we obtain the Central Limit Theorem and the Law of the Iterated Logarithm for a natural class of observables.


  • Tomasz SzarekInstitute of Mathematics
    Polish Academy of Sciences
    Abrahama 18
    81-967 Sopot, Poland
  • Anna ZdunikInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland

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