| Abstract |
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We consider implications of dynamical Borel-Cantelli lemmas for rates of
growth of Birkhoff sums of non-integrable observables
\(\phi(x)=d(x,q)^{-k}\), \(k>0\), 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.
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