Item description for Integrability and Nonintegrability of Dynamical Systems by Alain Goriely...
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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Studio: World Scientific Publishing Company
Est. Packaging Dimensions: Length: 1.25" Width: 6.5" Height: 9" Weight: 1.6 lbs.
Release Date Aug 15, 2001
Publisher World Scientific Publishing Company
ISBN 981023533X ISBN13 9789810235338
Reviews - What do customers think about Integrability and Nonintegrability of Dynamical Systems?
My book May 4, 2006
This is clearly the best book I've written so far and warmly recommend it to anybody interested in dynamical systems, integrability theory, Painleve theory and normal forms. A must read!
Formal and Comprehensive Exposition of Integrability Theory Dec 13, 2001
In his book, one of the goals of Dr. Goriely is to gather, classify and formalize all what is known about the theory of integrability for dynamical systems. Starting from the idea of a constant of motion for simple dynamical systems, it studies integrability from the geometrical and analytical point of view.
The first reason why I like this book is that, as far as I know, it is the first time someone presents the different results in integrability theory in such a formal and comprehensive way. For example, it is shown precisely why the well-known Painlevé test gives necessary conditions for the Painlevé Property to hold.
An other reason why I like this book is that as a mathematician it is the only place where I can find such an impresive amount of results on integrability gathered together in one single publication. Moreover, all those results are presented in a very comprehensive and pedagogical way. This book could be used for a graduate level course on integrability theory.
An other important aspect of the book is that it is not only restricted to integrability. For example, Dr. Goriely explores several aspects of how integrability techniques can be extended to the study nonintegrability.
To conclude, I think that such a book was missing in the mathematical literature and everyone specialized in integrability theory of will find it extremely useful.