The Conjugate Addition The Machine Topology To Embed The Necessary And Sufficient Condition For Topological Dynamical Systems

Dynamical system is an essential component of nonlinear science. Due to the fundmental work of Poincare, Lyapunov, Birkhoff and so on, dynamical system appears as an important branch of the modern mathematics of the richest achievements in 20th century. The dynamical system mainly investigates the limit behavior of the point under iteration. However, it is rather difficult to directly investigate the dynamical behavior of topological dynamical systems. Therefore, It is a very important and meaningful question to explore necessary and sufficient condition for the existence of a subsystem in the given topological dynamical system that is conjugate (resp., semi-conjugate) to the adding machine. We mainly investigate the necessary and sufficient condition for the existence of a subsystem in the given topological dynamical system that is conjugate (resp., semi-conjugate) to the adding machine. In essence,we use the adding machine to explore dynamical behavior of topological dynamical systems.In chapter 1 we mainly introduce the historical background of adding machine and the importance of the adding machine. The purpose and main results are also summarized in this chapter. In chapter 2 we give the general description of adding machine. In chapter 3 we give the main results, namely establish a necessary and sufficient condition for the existence of a subsystem in the given topological dynamical system that is conjugate (resp., semi-conjugate) to the adding machine. In Chapter 4 we summarize the results and innovation of this thesis, and present our view of perspectives for the future investigation of the adding machine.