Integrability and nonintegrability of dynamical systems
414 pages, parution le 10/12/2001
Résumé
This invaluable book examines qualitative and quantitative
methods for nonlinear differential equations, as well as
integrability and nonintegrability theory. Starting from
the idea of a constant of motion for simple systems of
differential equations, it investigates the essence of
integrability, its geometrical relevance and dynamical
consequences. Integrability theory is approached from
different perspectives, first in terms of differential
algebra, then in terms of complex time singularities and
finally from the viewpoint of phase geometry (for both
Hamiltonian and non-Hamiltonian systems). As generic
systems of differential equations cannot be exactly solved,
the book reviews the different notions of nonintegrability
and shows how to prove the nonexistence of exact solutions
and/or a constant of motion. Finally, nonintegrability
theory is linked to dynamical systems theory by showing how
the property of complete integrability, partial
integrability or nonintegrability can be related to regular
and irregular dynamics in phase space.
Table of Contents
- Integrability: An Algebraic Approach
- Integrability: An Analytic Approach
- Polynomial and Quasi-Polynomial Vector Fields
- Nonintegrability
- Hamiltonian Systems
- Nearly Integrable Dynamical Systems
- Open Problems
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | World Scientific |
| Auteur(s) | Alain Goriely |
| Parution | 10/12/2001 |
| Nb. de pages | 414 |
| Format | 15,5 x 22,,3 |
| Couverture | Relié |
| Poids | 740g |
| Intérieur | Noir et Blanc |
| EAN13 | 9789810235338 |
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