Poisson manifolds play a fundamental role in Hamiltonian dynamics, where they serve as phase spaces. They also arise naturally in other mathematical problems, and form a bridge from the "commutative world" to the "noncommutative world". The aim of this book is twofold: On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects, including singular foliations, Lie groupoids and Lie algebroids. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.
Progress in Mathematics Volume 242 Series Editor H. Bass J. Oesterlé A. Weinstein Jean-Paul Dufour Nguyen Tien Zung Poisson Structures and Their Normal Forms Birkhäuser Verlag Basel Boston Berlin Authors: Jean-Paul Dufour Département de mathématique Université de Montpellier 2 place Eugène Bataillon 34095 Montpellier France e-mail:
[email protected] Nguyen Tien Zung Laboratoire Émile Picard, UMR 5580 CNRS Institut de Mathématiques Université Paul Sabatier 118 route de Narbonne 31062 Toulouse France e-mail:
[email protected] 2000 Mathematics Subject Classification 53Dxx, 53Bxx, 85Kxx, 70Hxx A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publicatio