ENGLISH

Integrability and nonintegrability of dynamical systems

By Alain Goriely

Book information

Publisher
World Scientific
Year
2001
ISBN
9789810235338, 981023533X
Open Library ID
OL3579611M
Language
english
Format
PDF
Filesize
4 MB (4258243 bytes)
Series
Advanced series in nonlinear dynamics 19
Pages
291\291
Library
Kolxo3
Time added
2009-07-20 03:45:11

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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