7 papers
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…
An affirmative answer to Owings's sumset question
Wen Huang, Zhengxing Lian, Song Shao +3
We give an affirmative answer to Owings's sumset question: for any -coloring of natural numbers, there is an infinite such that is monochromatic. Mo…
Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers
Wen Huang, Song Shao, Tianyi Tao +2
In this paper we prove that for any finite coloring of N there are lambda,rho in N such that infinitely many pairs (x,y),(u,v) in N^2 satisfy the sets {lambda x, lambda y, x y, lam…
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…