拓扑空间中的拓扑共轭在迭代中的运用

On the Application of Iteration in the Topological Space of Topological Conjugacy

研究拓扑空间中的拓扑共轭在迭代中的性质及相关的运用,讨论了拓扑共轭的等价命题并给出了证明,指出了拓扑共轭的两个函数,可以看作同一个函数,在研究一个自映射的动力系统性质时,可以用与它拓扑共轭的较简单的自映射来代替,并给出了具体的应用。

This article is mainly about the nature and application of iteration in the topological space of topological conjugacy. It gives and proves the equivalent propositions of topological conjugacy. It is pointed out that if the two functions is topological conjugacy, then they can be regarded as the same functions. Then another simple topological conjugacy function can replace the function in the research of self-mapping properties of dynamical systems.