拓扑动力系统
拓扑动力系统 豆瓣
作者: 周作领//尹建东//许绍元 出版社: 科学出版社 2011
周作领、尹建东、许绍元所著的《拓扑动力系统——从拓扑方法到遍历理论方法》从线段动力系统、圆周动力系统、符号动力系统到一般动力系统,从纯拓扑方法到遍历理论方法,系统地介绍拓扑动力系统的基本内容,并结合这些基本内容的介绍,总结了作者30多年来在这些方面的科研成果。本书共分七章和三个附录,第1章在最一般意义下介绍拓扑动力系统的研究框架;第2章讨论一维(线段和圆周)动力系统;第3章讨论符号动力系统;从第4章,开始讨论一般动力系统,系统介绍从遍历理论基本思想引申出的几个基本问题,包括测度中心和极小吸引中心、弱和拟弱几乎周期点以及由此得到的点的轨道结构的三个层次等。本书主要讨论离散半动力系统,第7章把离散系统的弱几乎周期点概念推广到流的情形。前两个附录分别介绍必备的集合论和点集拓扑以及遍历理论知识,而附录C则是一篇深入讨论流的性质的文章。
《拓扑动力系统——从拓扑方法到遍历理论方法》可供数学专业高年级本科生和动力系统方向研究生、教师学习使用,亦可供相关专业科研人员和技术人员参考。
遍历性理论引论 豆瓣
作者: P.Walters 出版社: 世界图书出版公司 2003 - 6
In 1970 I gave a graduate course in ergodic theory at the University of Maryland in College Park, and these lectures were the basis of the Springer Lecture Notes in Mathematics Volume 458 called "Ergodic Theory--Introductory Lectures" which was published in 1975. This volume is nowout of print, so I decided to revise and add to the contents of these notes. I have updated the earlier chapters and have added some new chapters on the ergodic theory of continuous transformations of compact metric spaces. In particular, I have included some material on topological pressure and equilibrium states. In recent years there have been some fascinating interactions of ergodic theory with differentiable dynamics, differential geometry,number theory, von Neumann algebras, probability theory, statistical mechanics, and other topics. In Chapter 10 1 have briefly described some of these and given references to some of the others. I hope that this book will give the reader enough foundation to tackle the research papers on ergodictheory and its applications.