Some Dynamical Properties Of Nonautonomous Systems

Topological dynamical systems study mainly the qualitative proper-ties of actions of topological groups on general metric spaces. It is a very important branch of mathematics, and widely applied to physics, chem-istry, biology and other subjects. In recent years, the nonautonomous questions of nonlinear differential equations make the study of nonau-tonomous dynamical systems become a hot subject. On the subject this thesis does the following work:Chapter1introduces research background and current situation of classical dynamical systems and nonautonomous systems.Chapter2introduces some basic concepts and knowledge of dynami-cal systems.Chapter3gives three equivalent conditions of topological mixing and some conclusions of blending for an alternating system on a graph.Chapter4gives three equivalent conditions and some properties of topological transitivity for an alternating system, and some properties of recurrent set for a nonautonomous system on a compact metric space.Chapter5considers an uniformly convergent nonautonomous system, and gives a sufficient condition such that the limit system is Devaney chaotic.