UID:
almahu_9949199279702882
Format:
X, 308 p.
,
online resource.
Edition:
1st ed. 1990.
ISBN:
9783034892575
Note:
1. Preliminaries -- 1.1 A Simple Example: Motion in a Potential Field -- 1.2 Poisson Structure and Hamiltonian Systems -- 1.3 Symplectic Manifolds -- 1.4 Homogeneous Symplectic Spaces -- 1.5 The Moment Map -- 1.6 Hamiltonian Systems with Symmetry -- 1.7 Reduction of Hamiltonian Systems with Symmetry -- 1.8 Integrable Hamiltonian Systems -- 1.9 The Projection Method -- 1.10 The Isospectral Deformation Method -- 1.11 Hamiltonian Systems on Coadjoint Orbits of Lie Groups -- 1.12 Constructions of Hamiltonian Systems with Large Families of Integrals of Motion -- 1.13 Completeness of Involutive Systems -- 1.14 Hamiltonian Systems and Algebraic Curves -- 2. Simplest Systems -- 2.1 Systems with One Degree of Freedom -- 2.2 Systems with Two Degrees of Freedom -- 2.3 Separation of Variables -- 2.4 Systems with Quadratic Integrals of Motion -- 2.5 Motion in a Central Field -- 2.6 Systems with Closed Trajectories -- 2.7 The Harmonic Oscillator -- 2.8 The Kepler Problem -- 2.9 Motion in Coupled Newtonian and Homogeneous Fields -- 2.10 Motion in the Field of Two Newtonian Centers -- 3. Many-Body Systems -- 3.1 Lax Representation for Many-Body Systems -- 3.2 Completely Integrable Many-Body Systems -- 3.3 Explicit Integration of the Equations of Motion for Systems of Type I and V via the Projection Method -- 3.4 Relationship Between the Solutions of the Equations of Motion for Systems of Type I and V -- 3.5 Explicit Integration of the Equations of Motion for Systems of Type II and III -- 3.6 Integration of the Equations of Motion for Systems with Two Types of Particles -- 3.7 Many-Body Systems as Reduced Systems -- 3.8 Generalizations of Many-Body Systems of Type I-III to the Case of the Root Systems of Simple Lie Algebras -- 3.9 Complete Integrability of the Systems of Section 3.8 -- 3.10 Anisotropic Harmonic Oscillator in the Field of a Quartic Central Potential (the Garnier System) -- 3.11 A Family of Integrable Quartic Potentials Related to Symmetric Spaces -- 4. The Toda Lattice -- 4.1 The Ordinary Toda Lattice. Lax Representation. Complete Integrability -- 4.2 The Toda Lattice as a Dynamical System on a Coadjoint Orbit of the Group of Triangular Matrices -- 4.3 Explicit Integration of the Equations of Motion for the Ordinary Nonperiodic Toda Lattice -- 4.4 The Toda Lattice as a Reduced System -- 4.5 Generalized Nonperiodic Toda Lattices Related to Simple Lie Algebras -- 4.6 Toda-like Systems on Coadjoint Orbits of Borel Subgroups -- 4.7 Canonical Coordinates for Systems of Toda Type -- 4.8 Integrability of Toda-like Systems on Generic Orbits -- 5. Miscellanea -- 5.1 Equilibrium Configurations and Small Oscillations of Some Integrable Hamiltonian Systems -- 5.2 Motion of the Poles of Solutions of Nonlinear Evolution Equations and Related Many-Body Problems -- 5.3 Motion of the Zeros of Solutions of Linear Evolution Equations and Related Many-Body Problems -- 5.4 Concluding Remarks -- Appendix A -- Examples of Symplectic Non-Kählerian Manifolds -- Appendix B -- Solution of the Functional Equation (3.1.9) -- Appendix C -- Semisimple Lie Algebras and Root Systems -- Appendix D -- Symmetric Spaces -- References.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783764323363
Additional Edition:
Printed edition: ISBN 9783034892582
Language:
English
DOI:
10.1007/978-3-0348-9257-5
URL:
https://doi.org/10.1007/978-3-0348-9257-5
