Customer Reviews

Integrability and Nonintegrability of Dynamical Systems

5 star:		(2)
4 star:		(0)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

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!

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.