报告摘要：In this talk, we introduce some new notions of `periodic-like' points, such as almost periodic points, weakly almost periodic points, quasi-weakly almost periodic points, of free semigroup actions. We find that the corresponding sets and gap-sets of these points carry full upper capacity topological entropy of free semigroup actions under certain conditions. Furthermore, $\phi$-irregular set acting on free semigroup actions is introduced and it also carries full upper capacity topological entropy in the system with specification property. Finally, we introduce the level set for local recurrence of free semigroup actions and analyze its connections with upper capacity topological entropy. Our analysis generalizes the results obtained by Tian , Chen et al and Lau and Shu etc.

邀请人：赵云