Qualitative Theory of Differentiable Dynamical Systems（英文影印版）（硬皮精装）
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- 原书名：Qualitative Theory of Differentiable Dynamical Systems
- 作者： Shantao Liao
- 丛书名： 精装英文影印数学系列丛书
- 出版社：科学出版社
- ISBN：7030054377
- 上架时间：2006-8-18
- 出版日期：2006 年8月
- 开本：B5
- 页码：383
- 版次：1-1
- 所属分类：
数学 > 文科、经管、金融、工程数学 > 经济数学
内容简介回到顶部↑
professor liao shantao is an outstanding mathematician in china. as a result of his profound and systematic research work, he won the mathematics prize in 1985 which was the first time awarded by the third world academy of sciences for his contributions to differentiable dynamical systems and other fields. he also won first-class award of national natural science prize of china in 1987, the chinese edition of this book collects eight of his major articles on differentiable dynamical systems in the period of 1963 - 1984, arranged in the order according to the dates of submission for publications, together with a preface and an appendix written also by him. other two appendices a and b, which are original articles by liao, are added to the translation to the english edition. .
this book introduces systematically the derivation of the two fundamental notions of "standard systems of differential equations" and "obstruction sets" and exhibits their important properties and applications to stability problems. ...
this book introduces systematically the derivation of the two fundamental notions of "standard systems of differential equations" and "obstruction sets" and exhibits their important properties and applications to stability problems. ...
目录回到顶部↑
preface to the english edition
preface to the chinese edition.
chapter 1 certain ergodic properties of a differential system on a compact differentiable manifold
1.1 one-parameter transformation groups on frame bundles
1.2 covariant differentiation, the function ωk(α)
1.3 the function logζαk(t)
1.4 the style number k*(f)
1.5 on the determination of the style number
1.6 comparison of certain functions
1.7 3-dimensional systems with degenerate style numbers
1.8 square matrix rα(t) and divergence divs
references
chapter 2 standard systems of differential equations
2.1 a review of standard systems of differential equations
2.2 another class of standard systems of differential equations
2.3 families adp of differential equations
2.4 an application
references
chapter 3 obstruction sets and strong transversality condition
3.1 introduction
preface to the chinese edition.
chapter 1 certain ergodic properties of a differential system on a compact differentiable manifold
1.1 one-parameter transformation groups on frame bundles
1.2 covariant differentiation, the function ωk(α)
1.3 the function logζαk(t)
1.4 the style number k*(f)
1.5 on the determination of the style number
1.6 comparison of certain functions
1.7 3-dimensional systems with degenerate style numbers
1.8 square matrix rα(t) and divergence divs
references
chapter 2 standard systems of differential equations
2.1 a review of standard systems of differential equations
2.2 another class of standard systems of differential equations
2.3 families adp of differential equations
2.4 an application
references
chapter 3 obstruction sets and strong transversality condition
3.1 introduction
前言回到顶部↑
When we were young, I knew Prof. Liao Shantao very well through my classmate Prof. Sun Yifeng. In fact, we were all teaching in the Department of Mathematics of Peking University during the academic year 1946-1947. Both Liao and Sun participated in a seminar on topological groups conducted by Prof. Jiang Zehan, the pioneer of algebraic topology in China. Sun always told me much about Liao's genius in the theory of algebraic topology. His talk gave me deep impression that Liao should be a famous mathematician with great success in the theory of algebraic topology in the near future. While Liao returned from the U.S.A. to Peking University in 1956, he already became a famous topologist. However, Prof. Liao did not rest satisfied with his great success in algebraic topology. He paid more and more attention to the theory of differentiable dynamical systems in the beginning of the sixties of this century. Since then he wrote and published in Chinese a series of research articles on differentiable dynamical systems, which exhibit a remarkable characteristic of his own. There has long been a need of translation of his work into other languages, since the Chinese version of his work has already given great influence on the development of the theory of differentiable dynamical systems in China. I am glad that the National Natural Science Foundation of China has provided full support that makes the present English edition of this book available. .
This book is translated into English by his colleagues and students Dong Zhenxi, Gan Shaobo, Sun Wenxiang, Tang Yun, Wen Lan, Zhan Hansheng, and Zhang Meirong. While done individually, the translation of every chapter and appendix is just precise and honest to the original Chinese edition. Also notable is the work of Science Press, China that provides us with such a title volume. ...
Cheng Min-de
Member of the Chinese Academy of Sciences
Professor in Mathematics, Peking University
May 1996
This book is translated into English by his colleagues and students Dong Zhenxi, Gan Shaobo, Sun Wenxiang, Tang Yun, Wen Lan, Zhan Hansheng, and Zhang Meirong. While done individually, the translation of every chapter and appendix is just precise and honest to the original Chinese edition. Also notable is the work of Science Press, China that provides us with such a title volume. ...
Cheng Min-de
Member of the Chinese Academy of Sciences
Professor in Mathematics, Peking University
May 1996
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