Integrability and Nonintegrability of Dynamical Systems (Hardcover) (ISBN-13: 9789810235338)

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.

Author: Alain Goriely
ISBN-10: 981023533X
ISBN-13: 9789810235338
Publisher: World Scientific Publishing Company
Language: English
Published: 08/30/2001
Pages: 436
Format: Hardcover
Weight: 1.65lbs
Size: 8.60h x 6.38w x 1.18d

Review Citation(s):
Scitech Book News 12/01/2001 pg. 45