遍历性理论引论（影印版）
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- 原书名：An Introduction to Ergodic Theory
- 原出版社： Springer-Verlag
- 作者： Peter Walters
- 丛书名： Graduate Texts in Mathematics
- 出版社：世界图书出版公司
- ISBN：7506260093
- 上架时间：2004-9-30
- 出版日期：2003 年6月
- 开本：24开
- 页码：250
- 版次：1-1
- 所属分类：
数学 > 控制论,信息论
教材 > 研究生/本科/专科教材 > 理学 > 数学
内容简介回到顶部↑
书籍
数学书籍
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 now out 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 ergodic theory and its applications.
数学书籍
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 now out 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 ergodic theory and its applications.
目录回到顶部↑
chapter 0
preliminaries
0.1 introduction
0.2 measure spaces
0.3 integration
0.4 absolutely continuous measures and conditional expectations
0.5 function spaces
0.6 haar measure
0.7 character theory
0.8 endomorphisms of tori
0.9 perron-frobenius theory
0.10 topology
chapter 1
measure-preserving transformations
1.1 definition and examples
1.2 problems in ergodic theory
1.3 associated isometries
1.4 recurrence
1.5 ergodicity
1.6 the ergodic theorem
preliminaries
0.1 introduction
0.2 measure spaces
0.3 integration
0.4 absolutely continuous measures and conditional expectations
0.5 function spaces
0.6 haar measure
0.7 character theory
0.8 endomorphisms of tori
0.9 perron-frobenius theory
0.10 topology
chapter 1
measure-preserving transformations
1.1 definition and examples
1.2 problems in ergodic theory
1.3 associated isometries
1.4 recurrence
1.5 ergodicity
1.6 the ergodic theorem
前言回到顶部↑
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 now out 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 ergodic theory and its applications.
I would like to dedicate this volume to the memory of Rufus Bowen who died on July 30, 1978 at the age of 31. He made outstanding contributions to ergodic theory and his friendship enhancedthe lives of all who knew him.
April, 1981
PETER WALTERS
I would like to dedicate this volume to the memory of Rufus Bowen who died on July 30, 1978 at the age of 31. He made outstanding contributions to ergodic theory and his friendship enhancedthe lives of all who knew him.
April, 1981
PETER WALTERS
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