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国外数学名著系列(续一)51:动力系统Ⅶ可积系,不完整动力系统

国外数学名著系列(续一)51:动力系统Ⅶ可积系,不完整动力系统

作者:阿诺德
出版社:科学出版社出版时间:2016-03-24
开本: 16开 页数: 341
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国外数学名著系列(续一)51:动力系统Ⅶ可积系,不完整动力系统 版权信息

  • ISBN:9787030234940
  • 条形码:9787030234940 ; 978-7-03-023494-0
  • 装帧:一般胶版纸
  • 册数:暂无
  • 重量:暂无
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国外数学名著系列(续一)51:动力系统Ⅶ可积系,不完整动力系统 本书特色

This volume contains five surveys odynamical systems. The first one deals with nonholonomic mechanics and gives aupdated and systematic treatment of the geometry of distributions and of variational problems with nonintegrable constraints. The moderlanguage of differential geometry used throughout the survey allows for a clear and unified expositioof the earlier work ononholonomic problems. There is a detailed discussioof 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 Hamiltoniasystems, with aemphasis oLie-algebraic constructions. Among the topics covered are: the generalized Calogero-Moser systems based oroot systems of simple Lie algebras, a general r-matrix scheme for constructing integrable systems and Lax pairs, links with finite-gap integratiotheory, 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 representatiotheory.
  Readers will find all the new differential geometric and Liealgebraic methods which are currently used ithe theory of integrable systems ithis book. It will be indispensable to graduate students and researchers imathematics and theoretical physics.

国外数学名著系列(续一)51:动力系统Ⅶ可积系,不完整动力系统 内容简介

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国外数学名著系列(续一)51:动力系统Ⅶ可积系,不完整动力系统 目录

Introduction

Chapter 1. Geometry of Distributions
1. Distributions and Related Objects
1.1. Distributions and Differential Systems
1.2. Frobenius Theorem and the Flag of a Distribution
1.3. Codistributions and PfaffiaSystems
1.4. Regular Distributions
1.5. Distributions Invariant with Respect to Group Actions and Some Canonical Examples
1.6. Connections as Distributions
1.7. A Classificatioof Left Invariant Contact Structures oThree-Dimensional Lie Groups
2. Generic Distributions and Sets of Vector Fields. and Degeneracies of Small Codimension. Nilpotentizatioand ClassificatioProblem
2.1. Generic Distributions
2.2. Normal Forms of Jets of Basic Vector Fields of a GenericDistribution
2.3. Dcgeneracies of Small Codimension
2.4. Generic Sets of Vector Fields
2.5. Small CodimensioDegeneracies of Sets of Vector Fields
2.6. ProjectioMap Associated with a Distribution
2.7. Classificatoof Regular Distributions
2.8. Nilpotentizatioand Nilpotent Calculus

Chapter 2. Basic Theory of Nonholonomic RiemanniaManifolds
1. General Nonholonomic Variational Problem and the Geodesic
Flow oNonholonomic RiemanniaManifolds
1.1. Rashevsky-Chow Theorem and Nonholonomic Riemannian
Metrics (Carnot-Caratheodory Metrics)
1.2. Two-Point Problem and the Hopf-Rinow Theorem
1.3. The Cauchy Problem and the Nonholonomic Geodesic Flow
1.4. The Euler-Lagrange Equations iInvariant Form and ithe
Orthogonal Moving Frame and Nonholonomic Geodesics
1.5. The Standard Form of Equations of Nonholonomic Geodesics
for Generic Distributions
1.6. Nonholonomic Exponential Mapping and the Wave Front
1.7. The ActioFunctional
2. Estimates of the Accessibility Set
2.1. The Parallelotope Theorem
2.2. Polysystems and FinsleriaMetrics
2.3. Theorem othe Leading Term
2.4. Estimates of Generic Nonholonomic Metrics oCompact Manifolds
2.5. Hausdorff Dimensioof Nonholonomic RiemanniaManifolds
2.6. The Nonholonomic Ballithe Heisenbcrg Group as the Limit of Powers of a RiemanniaBall

Chapter 3. Nonholonomic Variational Problems onThree-Dimensional Lie Groups
1. The Nonholonomic E-Sphere and the Wave Front
1.1. Reductioof the Nonholonomic Geodesic Flow
1.2. Metric Tensors oThree-Dimensional Nonholonomic Lie Algebras
1.3. Structure Constants of Three-Dimensional Nonholonomic Lie Algebras
1.4. Normal Forms of Equations of Nonholonomic Geodesics oThree-Dimensional Lie Groups
1.5. The Flow othe Base V V1 of the Semidirect Product
1.6. Wave Front of Nonholonomic Geodesic Flow. Nonholonomic ε-Sphere and their Singularities
1.7. Metric Structure of the Sphere SeV
2. Nonholonomic Geodesic Flow oThree-Dimensional Lie Groups
2.1. The Monodromy Maps
2.2. Nonholonomic Geodesic Flow oSO(3)
2.3. NG-Flow oCompact Homogeneous Spaces of the Heisenberg Group
2.4. Nonholonomic Geodesic Flows oCompact Homogeneous Spaces of SL2R

References
Additional Bibliographical Notes
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