Topological Dynamical Systems And Symbolic Dynamical System Topologically Conjugate A Necessary And Sufficient Conditions

Since the twentieth century, dynamical system has been developed rapidly as a new discipline. And it mainly investigates the limit behavior of the point under iteration. Normally, It is very difficult to directly investigate the dynam-ical behavior of topological dynamical systems, and it is a common method to examine whether this system or its subsystem is topologically conjugate to a symbolic dynamical system or not. This paper gives a necessary and sufficient condition of topological conjugacy between topological dynamical systems and symbolic dynamical systems to provide a new tool of the investigation of topo-logical conjugacy.In chapter one we describe the historical background of topological dynam-ical system, and give the preliminaries and the author's work. In chapter two we mainly introduce the definition and importance of symbolic dynamical system. In chapter three we give the main theorem, namely, the necessary and sufficient condition of topological conjugacy between topological dynamical systems and symbolic dynamical systems. In chapter four we summarize the whole paper, and put forward some problems which can be further investigated.