Estimates for Correlation in Dynamical Systems: From Hölder Continuous Functions to General Observables

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Abstract

For many dynamical systems that are popular in applications, estimates are known for the decay of correlation in the case of Hölder continuous functions. In the present article, we suggest an approach that allows us to obtain estimates for correlation in dynamical systems in the case of arbitrary functions. This approach is based on approximation and estimates are obtained with the use of known estimates for Hölder continuous functions. We apply our approach to transitive Anosov diffeomorphisms and derive the central limit theorem for the characteristic functions of certain sets with boundary of zero measure.

Original languageEnglish
Pages (from-to)187-206
Number of pages20
JournalSiberian Advances in Mathematics
Volume28
Issue number3
DOIs
Publication statusPublished - 1 Jul 2018

Keywords

  • Anosov diffeomorphisms
  • approximation spaces
  • central limit theorem
  • correlation
  • the best approximation

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