Poisson Structures and Their Normal Forms

Jean-Paul Dufour, Nguyen Tien Zung (auth.), H. Bass, J. Oesterlé, A. Weinstein (eds.)3764373342, 9783764373344, 9783764373351, 3764373350

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.

Table of contents :
Generalities on Poisson Structures….Pages 1-37
Poisson Cohomology….Pages 39-75
Levi Decomposition….Pages 77-104
Linearization of Poisson Structures….Pages 105-128
Multiplicative and Quadratic Poisson Structures….Pages 129-157
Nambu Structures and Singular Foliations….Pages 159-201
Lie Groupoids….Pages 203-234
Lie Algebroids….Pages 235-262