半群作用的稠密小周期集系统与完全传递系统（英文）

Dense Small Periodic Sets and Total Transitivity of Semigroup Actions

称一个动力系统(S,X)具有稠密g-小周期集,如果对任意非空开集UX,存在非空闭子集YU和S的一个g-syndetic子半群T,使得TYY;称一个传递的动力系统(S,X)是g-完全传递的,如果对S的每一个g-syndetic子半群T,(T,X)都是传递的.本文指出,每一个具有稠密g-小周期集的g-完全传递系统(S,X)不交于任何极小系统,其中S是一个可数交换半群,S最多只有可数个g-syndetic子半群且S中的每一个元S都为X到自身的满射.

A dynamical system （S, X） is defined as a system with dense g-small periodic sets, if for every nonempty open subset U of X there exist a nonempty closed subset Y of U and a g-syndetic subsemigroup T of S such that TY C Y. A transitive dynamical system （S, X） is called g-totally transitive, if （T, X） is transitive for every g-syndetic subsemigroup T of S. In this article, we point out that every g-totally transitive dynanfical system （S,X） with dense g-small periodic sets is disjoint from all minimal systems, where S is a countable abelian semigroup, S has at most countably many g-syndetic subsemigroups and every s of S is a surjective map from X onto itself.