Integrable Systems of Classical Mechanics and Lie Algebras [EBook] : Volume I / by A. M. Perelomov.
Integrable Systems of Classical Mechanics and Lie Algebras [EBook] : Volume I / by A. M. Perelomov.
Personal Name(s):  Perelomov, A. M., (author) 

Imprint: 
Basel :
Birkhäuser,
1990

Physical Description: 
online resource. 
Note: 
englisch 
ISBN: 
9783034892575 
DOI: 
10.1007/9783034892575 
Subject (LOC):  
Full Text 
Table of Contents:
 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. ManyBody Systems
 3.1 Lax Representation for ManyBody Systems
 3.2 Completely Integrable ManyBody 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 ManyBody Systems as Reduced Systems
 3.8 Generalizations of ManyBody Systems of Type IIII 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 Todalike Systems on Coadjoint Orbits of Borel Subgroups
 4.7 Canonical Coordinates for Systems of Toda Type
 4.8 Integrability of Todalike 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 ManyBody Problems
 5.3 Motion of the Zeros of Solutions of Linear Evolution Equations and Related ManyBody Problems
 5.4 Concluding Remarks
 Appendix A
 Examples of Symplectic NonKählerian Manifolds
 Appendix B
 Solution of the Functional Equation (3.1.9)
 Appendix C
 Semisimple Lie Algebras and Root Systems
 Appendix D
 Symmetric Spaces
 References.