Recurrence theorem for multiplicative systems and applications

Abstract: Poincare recurrence theorem is one fundamental result in a dynamical system, which says that the orbit of a point on a measure-preserving system can visit the neighborhood of another point infinitely many times. Variations and applications of this theorem have been studied extensively in the literature. In this talk, we discuss the recurrence properties of a multiplicative system, i.e. a system admitting a multiplicative group action instead of a conventional additive group action. This is a direction that has not been studied much in the past, yet has many interesting applications. We will discuss recent progress on this topic, and its connections with problems in combinatorics and number theory.

Mathematics

Audience: researchers in the topic

ICCM 2020