几乎周期点稠密系统的研究

摘要

动力系统是紧致度量空间上的连续自映射.在动力系统理论中,全部重要的动力性态完全集中在它的测度中心上,研究极小性也就变为必然.极小性是从拓扑学的角度描述系统的不可分解性.因此,几乎周期性也是动力系统中一个非常重要的研究课题.而以下的研究正是从具有几乎周期性与稠密性这样的集合出发,构造了几乎周期点稠密系统.运用拓扑传递性与稠密性研究了几乎周期点稠密系统与Li-Yorke混沌的关系,以及几乎周期点稠密系统所具有的拓扑遍历性.这样建立起了几乎周期点稠密系统与拓扑遍历性的联系,对进一步了解几乎周期点稠密系统测度中心的性质有一定的启示作用.%Dynamical systems is the continuous self-mapping of a compact metric space. In the theory of dynamical systems, all important dynamic features are focused on the measure center, thus, researching on the minimality becomes inevitable. Minimality is the research on indecomposability from the aspect of dynamical systems. Therefore, almost periodic is one of the most important research topics on dynamical systems. Next, we start with almost periodic and density of sets, construct dense system of almost periodic points, and study the relation between almost periodic point dense system and Li-Yorke chaos by topological transitive and densityand topological ergodicity of almost periodic points dense systems. This established a contact of almost periodic points dense systems and topological ergodicity which has some inspiration to learn more about the nature of the measure center of almost periodic points dense systems.