Periodic Decompositions For Transitive And Minimal Group Actions

Topological dynamical systems study the qualitative properties of topological groups in topological space.The core problem of dynamical systems is the asymptotic property or topological structure of point orbit.In this paper,we study periodic decompositions for transitive and minimal group actions.Transitivity reflects the indecomposability of dynamic system.Specifically,the transitivity system cannot be decomposed into two disjoint sets with non-empty interiors.In chapter 3,we prove that the system with transitive group actions has a special decomposition for finite index normal subgroups,that is,the system is decomposed into some regular closed sets.The index of normal subgroups sets is divisible by the number of these closed.The intersection between closed sets is nowhere dense and maps to each other in a periodic manner.The actions of the finite index normal subgroups on any closed sets is transitive.Therefore,we define regular periodic decomposition of finite index subgroups and conclude a series of conclusions.Minimal system is a special transitive system,which reflects a stronger indecomposability of the system.In Chapter 4,we prove that the dynamical system under the minimal group actions has periodic decomposition similar to the above,and get relevant conclusions.