**SMF/AMS Texts and Monographs**

Volume: 15;
2008;
149 pp;
Softcover

MSC: Primary 70; 53; 12; 34; 14;
**Print ISBN: 978-0-8218-4413-7
Product Code: SMFAMS/15**

List Price: $60.00

Individual Member Price: $48.00

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#### Supplemental Materials

# Hamiltonian Systems and Their Integrability

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*Michèle Audin*

A co-publication of the AMS and Société Mathématique de France

Hamiltonian systems began as a mathematical approach to the study of
mechanical systems. As the theory developed, it became clear that the
systems that had a sufficient number of conserved quantities enjoyed
certain remarkable properties. These are the completely integrable
systems. In time, a rich interplay arose between integrable systems and
other areas of mathematics, particularly topology, geometry, and group
theory.

This book presents some modern techniques in the theory of integrable
systems viewed as variations on the theme of action-angle coordinates.
These techniques include analytical methods coming from the Galois theory
of differential equations, as well as more classical algebro-geometric
methods related to Lax equations.

Audin has included many examples and exercises. Most of the exercises
build on the material in the text. None of the important proofs have been
relegated to the exercises. Many of the examples are classical, rather
than abstract.

This book would be suitable for a graduate course in Hamiltonian
systems.

Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.

#### Readership

Graduate students interested in Hamiltonian and integrable systems.

#### Reviews & Endorsements

The book is addressed to graduate students without previous exposure to these topics … this is a refreshing attempt at giving a bird's eye view of disparate techniques that enter the geometric/differential nature of integrability of certain Hamiltonian systems. … The book is intended to be readable by a non-expert; … Several examples conclude each chapter, a good feature as they are workable and instructive …

-- Mathematical Reviews