Integrability and Nonintegrability of Dynamical Systems [Hardcover]

Alain Goriely (Author)

Book Description

Publication Date: August 15, 2001 | Series: Advanced Series in Nonlinear Dynamics, 19 (Book 19)

This work 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.

Editorial Reviews

Review

It is a nice introductory book for people interested in the field of the integrability of dynamical systems. -- Mathematics Abstracts

It is a valuable book and serves as a very useful tool for all researchers and as an educative textbook. -- Mathematical Reviews, 2002

Product Details

• Hardcover: 436 pages
• Publisher: World Scientific Pub Co Inc (August 15, 2001)
• Language: English
• ISBN-10: 981023533X
• ISBN-13: 978-9810235338
• Product Dimensions: 8.6 x 6.4 x 1.2 inches
• Shipping Weight: 1.6 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #5,316,883 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

5.0 out of 5 stars My book, May 4, 2006

By 

Alain Goriely - See all my reviews
(REAL NAME)   

This review is from: Integrability and Nonintegrability of Dynamical Systems (Hardcover)

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!

5.0 out of 5 stars Comprehensive Exposition of Integrability Theory and its Applications, December 12, 2001

By 

Stephane Lafortune (Charleston, sc) - See all my reviews

This review is from: Integrability and Nonintegrability of Dynamical Systems (Hardcover)

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.

The most important aspect of the book is that it is not only restricted to integrability. Dr. Goriely thoroughly explores how integrability techniques can be applied to dynamical systems in general.

To conclude, I think that such a book was missing in the mathematical literature and it is a must to everyone doing dynamical systems who would like to know more about the applications of the theory of integrability.