有向部分半群作用下的敏感性

The Sensitivity Under Directed Partial Semigroup Actions

在有向部分半群作用下,研究了动力系统的初值敏感性和n-敏感性,得到了初值敏感性和n-敏感性的若干结论:(1)对于紧致度量空间(X,d)上可交换的Λ-拓扑动力系统(X,{T}Λ),如果(X,{T}Λ)是传递的C系统,那么这个系统是几乎等度连续的当且仅当它不是敏感的.(2)对于Λ-拓扑动力系统(X,{T}Λ),如果X是局部连通空间,那么对于任意n≥2,(X,{T}Λ)是敏感的当且仅当它是n-敏感的.

The sensitivity and n-sensitivity are studied under directed partial semigroup actions,and some results about them are obtained.First,for an abelianΛ-topological dynamical system(X,{T}Λ)on compact metric space(X,d),if it is a transitive C-system,then it is almost equicontinuous if and only if it is non-sensitive.Se-cond,if(X,{T}Λ)is aΛ-topological dynamical system and X is a locally connected space,then(X,{T}Λ)is sensitive if and only if it is n-sensitive for every n≥2.