Research On Inseparability And Dynamical Systems On Symbolic Space

By generalizing transitivity, the concept of inseparability is presented. We show that on complete metric space, f is transitive if and only if f is inseparable and has no wandering points. Furthermore, the concepts of separability, finite-separability and totally-separability are presented to describe different level of separability. In fact, these properties are preserved under topological conjugacy and provide a method to classify dynamical systems.Model shift maps are a class of special chaotic maps on symbolic space and received much attention. In this paper, we proved that on one-sided symbolic space, model shift map is topologically conjugate with the traditional shift map. Also we found a kind of symbolic dynamical system with topological entropy log1.618, and it's topological mixing and chaos in the sense of Devaney. At last, we found a special map with the whole symbolic space as its minimal set and which is not chaos.