Discussion Of F Dense Chaos

In this paper,we study some properties on chaos of topological dynamical systems using the theorem of families. More precisely,In chapter 1,we briefly introduce the content,methods,development and present conditions in topological dynamical system,and main content in this paper.In chapter 2,we study the relations among F transitive, F equico-ntinuous and F uniformly rigid.In chapter 3,we introduce the notions of F sensitive and F Li-Yorke sensitive.Then we discuss the properties and relations among them.And we also study the properties among RPR_S,PR_S and LYR_S.In chapter 4,we introduce the notion of F dense chaos and give some equivalent conditions of F dense chaos. And then we study therelations among F scattering,F mixing and F- dense chaos.