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. |