Integrability And Nonintegrability Of Dynamical Systems
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Integrability And Nonintegrability Of Dynamical Systems

SKU: 9789812811943

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Additional information

Full Title

Integrability And Nonintegrability Of Dynamical Systems
Author(s)

Alain Goriely
Edition
ISBN

9789812811943, 9789810235338
Publisher

World Scientific
Format

PDF and EPUB

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.

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