Martingale–coboundary decomposition for families of dynamical systems

A. Korepanov, Z. Kosloff, I. Melbourne*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We prove statistical limit laws for sequences of Birkhoff sums of the type ∑j=0 n−1vn∘Tn j where Tn is a family of nonuniformly hyperbolic transformations. The key ingredient is a new martingale–coboundary decomposition for nonuniformly hyperbolic transformations which is useful already in the case when the family Tn is replaced by a fixed transformation T, and which is particularly effective in the case when Tn varies with n. In addition to uniformly expanding/hyperbolic dynamical systems, our results include cases where the family Tn consists of intermittent maps, unimodal maps (along the Collet–Eckmann parameters), Viana maps, and externally forced dispersing billiards. As an application, we prove a homogenisation result for discrete fast–slow systems where the fast dynamics is generated by a family of nonuniformly hyperbolic transformations.

Original languageAmerican English
Pages (from-to)859-885
Number of pages27
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Issue number4
StatePublished - Jul 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Masson SAS


  • Fast–slow systems
  • Homogenisation
  • Martingale–coboundary decomposition
  • Nonuniform hyperbolicity
  • Statistical limit laws


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