半群作用Li-Yorke对的存在性

On Li-Yorke pairs of semigroup actions

设X为紧度量空间,T为半群,本文研究了动力系统(X,T)上Li-Yorke对的存在性问题,证明了当(X,T)拓扑可迁且包含周期点时,在(X,T)上存在无限scrambled集.另外,列举了一些不包含Li-Yorke对的动力系统.

For a compact metric space X and a semigroup T,the existence of Li-Yorke pairs in dynamical system（X,T） is discussed.It is proved that if（X,T） is transitive and contains periodic points,then there is an infinite scrambled set in（X,T）.In addition,some dynamical systems containing no Li-Yorke pair are illustrated.