Some Researches On The Topological Sensitivity Of Topological Dynamical Systems

Sensitivity is an important concept in dynamical systems.In this thesis,some studies on the topological sensitivity and the complexity of some dynamics of dynamical systems and non-autonomous dynamical systems which are generalized by a continuous self-map acting on a topological space are carried out.The specific arrangements are as follows:The first chapter is an introduction,which briefly describes the research status of sensitivity of dynamical systems and non-autonomous dynamical systems and the background and source of questions considered in this thesis.The second chapter is divided into three parts: in the first part,the definition of topological sensitivity with respect to Furstenberg families of dynamical systems is introduced and the relevant conclusions are proved;in the second part,some properties and conclusions of n-topological sensitivity are obtained;in the third part,the concept of multi-sensitivity of dynamical systems is introduced and several conclusions of multi-sensitivity are proved.In the third chapter,the notions of topological sensitivity and some stronger forms of topological sensitivity of non-autonomous dynamical systems are introduced and the relations between sensitivity and weakly mixing as well as minimality are gotten.The fourth chapter is a summary and prospect of this thesis.In this chapter,a summary of the obtained results and some problems for us to consider in the future are presented.