Some Dynamical Properties of Syndetic Subsemigroups Actions
Some Dynamical Properties of Syndetic Subsemigroups Actions
复制标题
DOI：
10.1007/s10883-014-9246-3
复制
发表时间：
2015
影响因子：
0.9
通讯作者：
Huoyun Wang;Guifang Zhu;Yao Tang;Lin Huang
中科院分区：
文献类型：
--
作者：
Huoyun Wang;Guifang Zhu;Yao Tang;Lin Huang
本文研究了联合亚半群作用的一些动力学性质。我们证明，对于具有离散拓扑的作用交换半群的任何 s-联半群 T，T 的所有几乎周期点的集合等于 S 的所有几乎周期点的集合。我们通过g-syndedic子半群的包络推导了点传递半群作用的分解的一些陈述。如果 (T,X) 对于每个联联子半群TofS 都是传递的，则传递动力系统 (S,X) 被称为完全传递。我们指出，动力系统 (S,X) 是完全传递的当且仅当它与每个 s 周期系统弱不相交，其中 S 包含一个恒等式，并且每个 S 都是从 X 到自身的满射映射。
In this paper, some dynamical properties of syndetic subsemigroups actions are studied. We prove that for any s-syndetic subsemigroupTof the acting abelian semigroupSequipped with the discrete topology, the set of all almost periodic points ofTis equal to the set of all almost periodic points ofS. We deduce some statements on decomposition for point transitive semigroup actions by envelopes of g-syndedic subsemigroup. A transitive dynamical system (S,X) is called totally transitive if (T,X) is transitive for every syndetic subsemigroupTofS. We point out that a dynamical system (S,X) is totally transitive if and only if it is weakly disjoint from every s-periodic system, whereScontains an identity and everysofSis a surjective map fromXonto itself.