Advanced Series in Nonlinear Dynamics - Vol. 19
INTEGRABILITY AND NONINTEGRABILITY OF DYNAMICAL SYSTEMS
by Alain Goriely (University of Arizona, USA)
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.
Contents:
- Integrability: An Algebraic Approach
- Integrability: An
Analytic Approach
- Polynomial and Quasi-Polynomial Vector Fields
- Nonintegrability
- Hamiltonian Systems
- Nearly Integrable Dynamical Systems
- Open Problems
Readership: Mathematical and theoretical physicists and astronomers
and engineers interested in dynamical systems.
"It is a valuable book and serves as a very useful tool for all researchers working on these problems and, at the same time, as an educative textbook for anyone wishing to be introduced to the above theory."
| Mathematical Reviews, 2002 |
"It is a nice introductory book for people interested in the field of the integrability (and nonintegrability) of dynamical systems."
| 436pp |
Pub. date: Aug 2001 |
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