Dynamical Borel–Cantelli Lemma for Lipschitz Twists

Abstract: In the study of some dynamical systems, the limit superior of a sequence of measurable sets is often of interest. The shrinking targets and recurrence are two of the most commonly studied problems that concern limit superior sets. However, the zero-one laws for the shrinking targets and recurrence are usually treated separately and proved differently. In this talk, we construct a generalized definition that can specialize into the shrinking targets and recurrence and our approach gives a unified proof to the zero-one laws for the two problems.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar