乘积空间与拓扑群作用下逆极限空间的动力学性质-基础数学专业论文.docxVIP

(2) 设 ( X , d ) 是紧致度量 G- 空间，f : X ??X 同胚，f 的 Lipchitz 常数为 L ， ff ?1 的 Lipchitz 常数为 K ，系统 ( X f , G, d ,??) 是系统 ( X , G, d , f ) 的逆极限空间， 则 f 具有 G- 强跟踪性当且仅当??具有 G- 强跟踪性． 关键词： n 维乘积空间 乘积映射 G- 空间 Devaney G- 混沌  Korner 性质 G- 跟踪性 G- 强跟踪性 DYNAMICAL PROPERTY OF PRODUCT SPACE AND THE INVERSE LIMIT SPACE OF A TOPOLOGICAL GROUP ACTION ABSTRACT At present, it is very perfect to development of theory and result of dynamical system of one dimensional interval space and the inverse limit space But in pratical application, mathematical model of many subjects mainly belongs to iterative problems of self-map of high dimensional product space. At the same time, many scholars also meet the problem of dynamics in the inverse limit space of a topological group action. Hence it makes sense to study dynamical property of high dimensional product space and the inverse limit space of a topological group action. In this paper, we will further study these two aspects. In Chapter 3, we mainly gave 12 equivalent conditions of product map with closed periodic set in the n-dimensional product space. In Chapter 4, we will study Devaney G-chaos and G-korner property of shift map in the inverse limit space of a topological group action. We have the Let ( X , d ) be a compact metric G-space, f : X ??X be a homeomorphism map. The system ( X f , G, d ,??) is the inverse limit space of the system ( X , G, d , f ) . Then f is said be G-chaotic in the sense of Devaney if and only if??is said be G- chaotic in the sense of Devaney. Let ( X , d ) be a compact metric G-space, f : X ??X be a surjection. The system ( X f , G, d ,??) is the inverse limit space of the system ( X , G, d , f ) .Then f is said be G-korner if and only if??is said be G -korner. In Chapter 5, we will consider G -shadowing property and G -strong shadowing property of shift map in the inverse limit space of a topological group action. We have the following result: Let ( X , d ) be a compact metric G-space, f : X ??X be a surjective m