Research On Dynamics Of A Kind Of Lorenz Type Mappings

Since Lorenz published his famous article,many people have studied the Lorenz system, in the process of the research to the system,many new dynamical phenomena have been found and also a lot of research methods have been developed.In the second chapter,first physical background and the research status of the Lorenz system is introduced, and some classic literatures about the system are summarized,then Poincare mapping method is used to establish a nom-orientable Lorenz type map.The third chapter is mainly discussing dynamical characteristics of the non-orientable attractor of Lorenz type,first an attractor is constructed using the map which is given in the second chapter, then the attractor that is chaotic is proved in certain conditions, also the strange attractor is described by inverse limits,finally under some assumptions the attractor has hyperbolic structure is discussed.The fourth chapter is mainly about one-dimensional maps of Lorenz type, first some basic definition are introduced, then symbolic dynamics model of the one-dimensional maps of Lorenz type is given, further the conditions of topological transmission about this kind of maps is discussed,and the relationship between the topological entropy and the growth rate of the numbers of discontinuous points during iteration progress is proved, then kneading sequences is used to deduce the calculation formula of the topological entropy of the maps, finally the method of subshift of finite type to compute topological entropy is introduced.