基本信息
- 原书名：Dynamical Systems VII: Integrable Systems Nonholonomic Dynamical Systems
- 原出版社： Springer
- 作者： V. I. Arnol'D S. P. Novikov
- 丛书名： 国外数学名著系列
- 出版社：科学出版社
- ISBN：9787030234940
- 上架时间：2014-6-25
- 出版日期：2009 年1月
- 开本：16开
- 页码：341
- 版次：1-1
- 所属分类：数学 > 动力系统理论
内容简介
书籍
数学书籍
This volume contains five surveys on dynamical systems. The first one deals with nonholonomic mechanics and gives an updated and systematic treatment of the geometry of distributions and of variational problems with nonintegrable constraints. The modern language of differential geometry used throughout the survey allows for a clear and unified exposition of the earlier work on nonholonomic problems. There is a detailed discussion of the dynamical properties of the nonholonomic geodesic flow and of various related concepts, such as nonholonomic exponential mapping, nonholonomic sphere, etc. .
Other surveys treatvarious aspects of integrable Hamiltonian systems, with an emphasis on Lie-algebraic constructions. Among the topics covered are: the generalized Calogero-Moser systems based on root systems of simple Lie algebras, a general r-matrix scheme for constructing integrable systems and Lax pairs, links with finite-gap integration theory, topological aspects ofintegrable systems, integrable tops, etc. One of the surveys gives a thorough analysis of a family of quantum integrable systems(Toda lattices)using the machinery of representation theory. ..
Readers will find all the new differential geometric and Liealgebraic methods which are currently used in the theory of integrable systems in this book. It will be indispensable to graduate students and researchers in mathematics and theoretical physics. ...
数学书籍
This volume contains five surveys on dynamical systems. The first one deals with nonholonomic mechanics and gives an updated and systematic treatment of the geometry of distributions and of variational problems with nonintegrable constraints. The modern language of differential geometry used throughout the survey allows for a clear and unified exposition of the earlier work on nonholonomic problems. There is a detailed discussion of the dynamical properties of the nonholonomic geodesic flow and of various related concepts, such as nonholonomic exponential mapping, nonholonomic sphere, etc. .
Other surveys treatvarious aspects of integrable Hamiltonian systems, with an emphasis on Lie-algebraic constructions. Among the topics covered are: the generalized Calogero-Moser systems based on root systems of simple Lie algebras, a general r-matrix scheme for constructing integrable systems and Lax pairs, links with finite-gap integration theory, topological aspects ofintegrable systems, integrable tops, etc. One of the surveys gives a thorough analysis of a family of quantum integrable systems(Toda lattices)using the machinery of representation theory. ..
Readers will find all the new differential geometric and Liealgebraic methods which are currently used in the theory of integrable systems in this book. It will be indispensable to graduate students and researchers in mathematics and theoretical physics. ...
目录
Ⅰ. Nonholonomic Dynamical Systems, Geometry of Distributions and Variational Problems .
Ⅱ. Integrable Systems Ⅱ
Chapter 1 Integrable Systems and Finite-Dimensional Lie Algebras
Chapter 2 Group-Theoretical Methods in the Theory of Finite-Dimensional Integrable Systems ..
Chapter 3 Quantization of Open Toda Lattices
Ⅲ. Geometric and Algebraic Mechanisms of the Integrability of Hamiltonian Systems on Homogeneous Spaces and Lie Algebras
Author Index
Subject Index ...
Ⅱ. Integrable Systems Ⅱ
Chapter 1 Integrable Systems and Finite-Dimensional Lie Algebras
Chapter 2 Group-Theoretical Methods in the Theory of Finite-Dimensional Integrable Systems ..
Chapter 3 Quantization of Open Toda Lattices
Ⅲ. Geometric and Algebraic Mechanisms of the Integrability of Hamiltonian Systems on Homogeneous Spaces and Lie Algebras
Author Index
Subject Index ...
