动力系统存在转移不变集的条件

Conditions of Topological Dynamical System Contain Transitive Invariant Set

研究一般拓扑动力系统的复杂性是很困难的。拓扑共轭、拓扑半共轭、嵌入映射和转移不变集都可以不同程度保持动力系统的复杂性。本文通过研究拓扑动力系统与符号动力系统拓扑共轭,找到了拓扑动力(子)系统存在转移不变集的条件,这样就可以通过研究相对简单和形象的符号动力系统,间接的反应一般拓扑动力(子)系统的动力性状。

It is difficult to study complexity behaviors of generally topological dynamical system. Topological conjugation, topological semi conjugation, embedding map and Transitive invariant set can make some properties and characteristics of topological dynamical system not change. The purpose of this paper is to study the conditions of exist subsystems topologically （semi） conjugate to symbolic dynamical systems. Then it can study the complexity behaviors of symbolic dynamical system to find out the properties and characteristics of topological dynamical system.