Integrability and Nonintegrability of Dynamical Systems

This book examines qualitative and quantitative methods for nonlinear differential equations and treats 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 its 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). The book reviews different ideas of nonintegrability and shows how to prove the nonexistence of exact solutions. Annotation c. Book News, Inc., Portland, OR (booknews.com)