Martingale-coboundary decomposition for families of dynamical systems
Korepanov, A; Kosloff, Z; Melbourne, I
Date: 8 September 2017
Journal
Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire
Publisher
Elsevier
Publisher DOI
Abstract
We prove statistical limit laws for sequences of Birkhoff sums of the type ∑j=0n-1vn(ring operator)Tnj 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 ...
We prove statistical limit laws for sequences of Birkhoff sums of the type ∑j=0n-1vn(ring operator)Tnj 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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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