Dynamical Borel–Cantelli lemmas and rates of growth of Birkhoff sums of non-integrable observables on chaotic dynamical systems. (7th June 2017)

• Record Type: Journal Article
• Authors: Carney, Meagan; Nicol, M
• Is Part Of: Nonlinearity. Volume 30:Number 7(2017:Jul.)
• Page Start: 2854
• Page End: 2870
• Publication Date: 2017-06-07
• Subjects: infinite ergodic theory -- Birkhoff sums -- Dynamical Borel–Cantelli lemmas; 37A99 -- 37A50 -- 60F99; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa72c2
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider implications of dynamical Borel–Cantelli lemmas for rates of growth of Birkhoff sums of non-integrable observables φ ( x ) = d ( x, q ) − k, k > 0, on ergodic dynamical systems ( T, X, μ ) where μ ( X ) = 1 . Some general results are given as well as some more concrete examples involving non-uniformly expanding maps, intermittent type maps as well as uniformly hyperbolic systems.