强传递的新特征

New characterization of strongly transitive

动力系统是一门关于时间演化规律的数学学科,其中由紧致拓扑空间的连续自映射给出的动力系统的传递性一直以来都是动力系统研究的一个重要课题.令(X,f)是一个动力系统,对于X中任意的两个非空开子集U和V,若存在整数n≥0,使得U∩f-nV≠?,则称(X,f)是拓扑传递的.运用N-开子集,定义几种新的拓扑传递的加强形式,研究并分别证明其多种等价命题,旨在开集的弱形式下得到一些动力学性质.

Dynamical system is a mathematical subject about the law of time evolution.The transitivity of dynamical system given by continuous self-mapping of compact topological space has always been an important subject in the study of dynamical system.Let(X,f)be a topological dynamical,it is said to be topological transitivity if for every pair of non-empty open set U and V,there existed n≥0,such thatU∩f-nV≠?.In this thesis,we defined several new strengthened forms of topological transfer by using N-open subsets,studied and proved their multiple equivalent propositions separately.Some dynamical properties in the weak form of the open set were obtained.