拓扑动力系统中强传递集的一些性质  

Some Properties of Strong Transitive Sets on Topological Dynamical System

作　　者：李瑞佳 朱培勇[1] 

机构地区：[1]电子科技大学数学科学学院,成都611731

出　　处：《四川理工学院学报（自然科学版）》2016年第6期90-93,共4页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金(11501391)

摘　　要：在拓扑动力系统中传递集的基础上引入强传递集的概念。首先证明强传递集是严格强于传递集的,然后证明两个强传递集的并是强传递的,但传递集没有类似结果。在拓扑动力系统(X,f)中分别讨论强传递集与传递点集、回复点集、轨道集、映射传递之间的关系,得到了存在点x∈X使得x∈Rec(f),但{x}不是强传递集,以及映射f是传递的当且仅当X中的任意非空开集为强传递集等一些等价刻画和充分性结果,并且在符号动力系统中利用强传递集证明了任意有限长度柱形都为传递集,从而推广了相关文献得到的结果,最后通过反例证明了强传递集与映射传递集Transf是互不蕴含的。The concept of strong transitive sets on the basis of transitive sets in topological dynamical systems are introduced. First,it is proved that the strong transitive set is strictly stronger than the transitive set,and then it is proved that the union of two strong transitive sets is strong transitive set,but the transitive sets have no similar results. Then,the relationships between the strong transitive set,the transitive point set,the recurrent point set,the orbit set,and the transitive map in topological dynamical systems（ X,f） are discussed. The x ∈ X such that x ∈ Rec（ f）,but { x} is not a strong transitive set,and the mapping of f is transitive if and only if the arbitrary nonempty open set is strong transitive set and so on. Besides,some equivalent characterizations and sufficient results are obtained. And in the symbolic dynamical system,the strong transitive set is used to prove that any finite length cylinder is a transitive set,which generalizes a result obtained by Liu Lei in the near future. Finally,the counter example shows that strong transitive set and Transfare not implied in each other.

关 键 词：拓扑动力系统 强传递集 符号动力系统 

分 类 号：O189.11[理学—数学]