Slow polynomial mixing, dynamical Borel-Cantelli lemma and Hausdorff dimension of dynamical diophantine sets

Abstract

In this article, we establish optimality results regarding the dynamical Borel-Cantelli lemma and the the Hausdorff dimension of certain dynamical diophantine sets.

This version corrects a typo in the definition of S_α, ${\chi }_{[0,1)}$ is now replaced by ${\chi }_{[0,\frac{1}{2})}$