A generalized multiple Borel-Cantelli lemma in dynamics and its applications

The multiple Borel-Cantelli lemma is a criterion that characterizes the occurrence of multiple rare events on the same time scale. In this work, we extend the version of the multiple Borel-Cantelli lemma in dynamics, as established by Dolgopyat, Fayad and Liu [J. Mod. Dyn. 18 (2022) 209-289], thus broadening its applicability to several non-smooth systems preserving absolutely continuous measures. Using this generalization, we establish multiple logarithm laws for hitting time and recurrence for dispersing billiard maps and piecewise expanding maps under certain regular conditions, including tent maps, Lorenz-like maps and the Gauss map.