国外数学名著系列（续一）（影印版）51：动；力系统Ⅶ可积系统，不完整动力系统
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作者： （俄罗斯）阿诺德等编著
出 版 社： 科学出版社
出版时间： 2009-1-1字数： 430000版次： 1页数： 341印刷时间： 2009/01/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9787030234940包装： 精装编辑推荐
要使我国的数学事业更好地发展起来，需要数学家淡泊名利并付出更艰苦地努力。另一方面，我们也要从客观上为数学家创造更有利的发展数学事业的外部环境，这主要是加强对数学事业的支持与投资力度，使数学家有较好的工作与生活条件，其中也包括改善与加强数学的出版工作。
这次科学出版社购买了版权，一次影印了23本施普林格出版社出版的数学书，就是一件好事，也是值得继续做下去的事情。大体上分一下，这23本书中，包括基础数学书5本，应用数学书6本与计算数学书12本，其中有些也具有交叉性质。
这些书可以使读者较快地了解数学某方面的前沿，对从事这方面研究的数学家了解该领域的前沿与全貌也很有帮助。
内容简介
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
