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

Abstract

We consider implications of dynamical Borel-Cantelli lemmas for rates of growth of Birkhoff sums of non-integrable observables $\phi (x)=d(x,p{)}^{-k}$, $k>0$, on ergodic dynamical systems $(T,X,\mu )$ where $\mu (X)=1$. 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.

20 pages, 8 figures

References in corpus (1)

• A Borel-Cantelli lemma for intermittent interval maps

Cited by in corpus (2)

• Pointwise convergence of Birkhoff averages for global observables
• Strong laws of large number for intermediately trimmed Birkhoff sums of observables with infinite mean