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arXiv · 1611.03540

Dynamical Borel-Cantelli lemmas and rates of growth of Birkhoff sums of non-integrable observables on chaotic dynamical systems

Meagan Carney·Matthew Nicol
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Abstract

We consider implications of dynamical Borel-Cantelli lemmas for rates of growth of Birkhoff sums of non-integrable observables $φ(x) = d(x,p)^{-k}$, $k>0$, 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.

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Meagan Carney, Matthew Nicol. 2016-11-10. Dynamical Borel-Cantelli lemmas and rates of growth of Birkhoff sums of non-integrable observables on chaotic dynamical systems. https://doi.org/10.1088/1361-6544%2Faa72c2

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