《動力系統Ⅶ：可積系統，不完整動力系統》是2009年科學出版社出版的圖書，作者是阿諾德 (V.I.Arnol'd)、s.p.novikov。
基本介紹
- 書名：動力系統Ⅶ：可積系統，不完整動力系統
- 作者：阿諾德 (V.I.Arnol'd)、s.p.novikov
- ISBN：9787030234940
- 頁數：341
- 定價：80.00元
- 出版社：科學出版社
- 出版時間：2009-1
- 叢書： 國外數學名著系列
內容介紹,編輯推薦,圖書目錄,
內容介紹
《國外數學名著系列(續一)(影印版)51:動力系統7(可積系統,不完整動力系統)》主要內容：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.
編輯推薦
《國外數學名著系列(續一)(影印版)51:動力系統7(可積系統,不完整動力系統)》由科學出版社出版。
要使我國的數學事業更好地發展起來，需要數學家淡泊名利並付出更艱苦地努力。另一方面，我們也要從客觀上為數學家創造更有利的發展數學事業的外部環境，這主要是加強對數學事業的支持與投資力度，使數學家有較好的工作與生活條件，其中也包括改善與加強數學的出版工作。
這次科學出版社購買了著作權，一次影印了23本施普林格出版社出版的數學書，就是一件好事，也是值得繼續做下去的事情。大體上分一下，這23本書中，包括基礎數學書5本，套用數學書6本與計算數學書12本，其中有些也具有交叉性質。
這些書可以使讀者較快地了解數學某方面的前沿，對從事這方面研究的數學家了解該領域的前沿與全貌也很有幫助。
要使我國的數學事業更好地發展起來，需要數學家淡泊名利並付出更艱苦地努力。另一方面，我們也要從客觀上為數學家創造更有利的發展數學事業的外部環境，這主要是加強對數學事業的支持與投資力度，使數學家有較好的工作與生活條件，其中也包括改善與加強數學的出版工作。
這次科學出版社購買了著作權，一次影印了23本施普林格出版社出版的數學書，就是一件好事，也是值得繼續做下去的事情。大體上分一下，這23本書中，包括基礎數學書5本，套用數學書6本與計算數學書12本，其中有些也具有交叉性質。
這些書可以使讀者較快地了解數學某方面的前沿，對從事這方面研究的數學家了解該領域的前沿與全貌也很有幫助。
圖書目錄
Introduction
Chapter 1. Geometry of Distributions
I. Distributions and Related Objects
1.1. Distributions and Differential Systems
1.2. Frobenius Theorem and the Flag of a Distribution
1.3. Codistributions and Pfaffian Systems
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 Classification of Left Invariant Contact Structures on Three-Dimensional Lie Groups
2. Generic Distributions and Sets of Vector Fields, and Degeneracies of Small Codimension. Nilpotentization and Classification Problem
2.1. Generic Distributions
2.2. Normal Forms of Jets of Basic Vector Fields of a Generic Distribution
2.3. Degeneracies of Small Codimension
2.4. Generic Sets of Vector Fields
2.5. Small Codimension Degeneracies of Sets of Vector Fields
2.6. Projection Map Associated with a Distribution
2.7. Classificaton of Regular Distributions
2.8. Nilpotentization and Nilpotent Calculus
Chapter 2. Basic Theory of Nonholonomic Riemannian Manifolds
1. General Nonholonomic Variational Problem and the Geodesic
Flow on Nonholonomic Riemannian Manifolds
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 in Invariant Form and in the 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 Action Functional
2. Estimates of the Accessibility Set
2.1. The Parallelotope Theorem
2.2. Polysystems and Finslerian Metrics
2.3. Theorem on the Leading Term
2.4. Estimates of Generic Nonholonomic Metrics on CompactManifolds
2.5. Hausdorff Dimension of Nonholonomic Riemannian Manifold!
2.6. The Nonhoionomic Ball in the Heisenberg Group as the Limit of Powers of a Riemannian Ball
Chapter 3. Nonhoionomic Variational Problems on Three-Dimensional Lie Groups
1. The Nonholonomic e-Sphere and the Wave Front
1.1. Reduction of the Nonhoionomic Geodesic Flow
1.2. Metric Tensors on Three-Dimensional Nonholonomic Lie Algebras
1.3. Structure Constants of Three-Dimensional Nonholonomic Lie Algebras
1.4. Normal Forms of Equations of Nonholonomic Geodesics on Three-Dimensional Lie Groups
1.5. The Flow on the Base V + Vl of the Semidirect Product
1.6. Wave Front of Nonholonomic Geodesic Flow, Nonholonomic e-Sphere and their Singularities
1.7. Metric Structure of the Sphere
2. Nonholonomic Geodesic Flow on Three-Dimensional Lie Groups
2.1. The Monodromy Maps
2.2. Nonholonomic Geodesic Flow on SO(3)
2.3. NG-Fiow on COmpact Homogeneous Spaces of the Heisenberg Group
2.4. Nonholonomic Geodesic Flows on Compact HomogeneousSpaces of SL
2.5. Nonholonomic Geodesic Flow on Some SpecialMultidimensional Nilmanifolds
References
Additional Bibliographical Notes
Chapter 1. Geometry of Distributions
I. Distributions and Related Objects
1.1. Distributions and Differential Systems
1.2. Frobenius Theorem and the Flag of a Distribution
1.3. Codistributions and Pfaffian Systems
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 Classification of Left Invariant Contact Structures on Three-Dimensional Lie Groups
2. Generic Distributions and Sets of Vector Fields, and Degeneracies of Small Codimension. Nilpotentization and Classification Problem
2.1. Generic Distributions
2.2. Normal Forms of Jets of Basic Vector Fields of a Generic Distribution
2.3. Degeneracies of Small Codimension
2.4. Generic Sets of Vector Fields
2.5. Small Codimension Degeneracies of Sets of Vector Fields
2.6. Projection Map Associated with a Distribution
2.7. Classificaton of Regular Distributions
2.8. Nilpotentization and Nilpotent Calculus
Chapter 2. Basic Theory of Nonholonomic Riemannian Manifolds
1. General Nonholonomic Variational Problem and the Geodesic
Flow on Nonholonomic Riemannian Manifolds
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 in Invariant Form and in the 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 Action Functional
2. Estimates of the Accessibility Set
2.1. The Parallelotope Theorem
2.2. Polysystems and Finslerian Metrics
2.3. Theorem on the Leading Term
2.4. Estimates of Generic Nonholonomic Metrics on CompactManifolds
2.5. Hausdorff Dimension of Nonholonomic Riemannian Manifold!
2.6. The Nonhoionomic Ball in the Heisenberg Group as the Limit of Powers of a Riemannian Ball
Chapter 3. Nonhoionomic Variational Problems on Three-Dimensional Lie Groups
1. The Nonholonomic e-Sphere and the Wave Front
1.1. Reduction of the Nonhoionomic Geodesic Flow
1.2. Metric Tensors on Three-Dimensional Nonholonomic Lie Algebras
1.3. Structure Constants of Three-Dimensional Nonholonomic Lie Algebras
1.4. Normal Forms of Equations of Nonholonomic Geodesics on Three-Dimensional Lie Groups
1.5. The Flow on the Base V + Vl of the Semidirect Product
1.6. Wave Front of Nonholonomic Geodesic Flow, Nonholonomic e-Sphere and their Singularities
1.7. Metric Structure of the Sphere
2. Nonholonomic Geodesic Flow on Three-Dimensional Lie Groups
2.1. The Monodromy Maps
2.2. Nonholonomic Geodesic Flow on SO(3)
2.3. NG-Fiow on COmpact Homogeneous Spaces of the Heisenberg Group
2.4. Nonholonomic Geodesic Flows on Compact HomogeneousSpaces of SL
2.5. Nonholonomic Geodesic Flow on Some SpecialMultidimensional Nilmanifolds
References
Additional Bibliographical Notes
