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Multi-Hamiltonian Theory of Dynamical Systems [Hardback]

  • Formāts: Hardback, 353 pages, 5 figures
  • Sērija : Texts and Monographs in Physics
  • Izdošanas datums: 30-Jul-1998
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 354064251X
  • ISBN-13: 9783540642510
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Multi-Hamiltonian Theory of Dynamical SystemsPalielināt
  • Formāts: Hardback, 353 pages, 5 figures
  • Sērija : Texts and Monographs in Physics
  • Izdošanas datums: 30-Jul-1998
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 354064251X
  • ISBN-13: 9783540642510
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783540642510.html
This is a modern Hamiltonian theory offering a unified treatment of all types of systems (finite, lattice and field). Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single co-ordinate system. As this property is closely related to integrability, this book presents an algebraic theory of integrable systems. It is intended for scientists, lecturers and students interested in the field.
1. Preliminary Considerations
1(12)
2. Elements of Differential Calculus for Tensor Fields
13(28)
2.1 Tensors
13(3)
2.2 Tensor Fields
16(2)
2.3 Transformation Properties of Tensor Fields
18(5)
2.4 Directional Derivative of Tensor Fields
23(4)
2.5 Differential k-Forms
27(5)
2.6 Flows and Lie Transport
32(2)
2.7 Lie Derivatives
34(7)
3. The Theory of Hamiltonian and Bi-Hamiltonian Systems
41(46)
3.1 Lie Algebras
42(7)
3.2 Hamiltonian and Bi-Hamiltonian Vector Fields
49(3)
3.3 Symmetries and Conserved Quantities of Dynamical Systems
52(4)
3.4 Tensor Invariants of Dynamical Systems
56(7)
3.5 Algebraic Properties of Tensor Invariants
63(20)
3.6 The Miura Transformation
83(4)
4. Lax Representations of Multi-Hamiltonian Systems
87(20)
4.1 Lax Operators and Their Spectral Deformations
88(3)
4.2 Lax Representations of Isospectral and Nonisospectral Hierarchies
91(10)
4.3 The Lax Operator Algebra
101(6)
5. Soliton Particles
107(28)
5.1 General Aspects
107(2)
5.2 Algebraic Structure of Linear Systems
109(8)
5.3 Algebraic Structure of Multi-Soliton Representation
117(13)
5.4 Multi-Soliton Perturbation Theory
130(5)
6. Multi-Hamiltonian Finite Dimensional Systems
135(114)
6.1 Stationary Flows of Infinite Systems. Ostrogradsky Parametrizations
137(14)
6.2 Stationary Flows of Infinite Systems. Newton Parametrization
151(15)
6.3 Constrained Flows of Lax Equations
166(11)
6.4 Restricted Flows of Infinite Systems
177(7)
6.5 Separability of Bi-Hamiltonian Chains with Degenerate Poisson Structures
184(36)
6.6 Nonstandard Multi-Hamiltonian Structures and Their Finite Dimensional Reductions
220(21)
6.7 Bi-Hamiltonian Chains on Poisson-Nijenhuis Manifolds
241(8)
7. Multi-Hamiltonian Lax Dynamics in (1+1)-Dimensions
249(64)
7.1 Hamiltonian Dynamics on Lie Algebras
250(7)
7.2 Basic Facts About R-Structures
257(7)
7.3 Multi-Hamiltonian Dynamics of Pseudo-Differential Lax Operators
264(29)
7.4 Multi-Hamiltonian Dynamics of Shift Lax Operators
293(20)
8. Towards a Multi-Hamiltonian Theory of (2+1)-Dimensional Field Systems
313(24)
8.1 The Sato Theory
313(12)
8.2 Multi-Hamiltonian Lax Dynamics for Noncommutative Variables
325(12)
References 337(10)
Index 347