7 papers · 1 filter
Rigid Functions, IP-Systems, and Topological Mild Mixing
Song Shao, Hui Xu
We study uniform rigidity and topological mild mixing through continuous observables. For a fixed sequence of times, the observables rigid along that sequence form a closed unital…
Adherence Semigroups and Density Finite-Sums Configurations
Song Shao, Hui Xu
In this paper, we use the adherence semigroup to describe finite-sums configurations in topological dynamical systems. We establish a correspondence between exact finite sumsets an…
Structure theorems of commuting transformations and minimal -flows
Song Shao, Hui Xu
In this paper, we develop several structure theorems concerning commuting transformations and minimal -flows. Specifically, we show that if , are minimal…
On systems disjoint from all minimal systems
Wen Huang, Song Shao, Hui Xu +1
Recently, Górska, LemaÅczyk, and de la Rue characterized the class of automorphisms disjoint from all ergodic automorphisms. Inspired by their work, we provide several characteri…
Pointwise convergence of some continuous-time polynomial ergodic averages
Wen Huang, Song Shao, Rongzhong Xiao
In this paper, we study the pointwise convergence of centain continuous-time polynomial ergodic averages. Our approach is based on the topological models of measurable flows. One o…
Multiple recurrence without commutativity
Wen Huang, Song Shao, Xiangdong Ye
We study multiple recurrence without commutativity in this paper. We show that for any two homeomorphisms with and being minimal, there is a r…