| Integrability and Nonintegrability of Dynamical Systems Contributor(s): Goriely, Alain (Author) |
|
 |
ISBN: 981023533X ISBN-13: 9789810235338 Publisher: World Scientific Publishing Company OUR PRICE: $149.15 Product Type: Hardcover Published: August 2001 |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Medical |
| Dewey: 530.151 |
| LCCN: 2002265621 |
| Series: Advanced Series in Nonlinear Dynamics |
| Physical Information: 1.18" H x 6.38" W x 8.6" (1.65 lbs) 436 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |