Martingale–coboundary decomposition for families of dynamical systems
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 859-885.

We prove statistical limit laws for sequences of Birkhoff sums of the type j=0n1vnTnj 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.

DOI : 10.1016/j.anihpc.2017.08.005
Mots clés : Martingale–coboundary decomposition, Nonuniform hyperbolicity, Statistical limit laws, Homogenisation, Fast–slow systems
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Korepanov, A.; Kosloff, Z.; Melbourne, I. Martingale–coboundary decomposition for families of dynamical systems. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 859-885. doi : 10.1016/j.anihpc.2017.08.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2017.08.005/

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