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

Meagan Carney, Matthew Nicol

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 sys…