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Poisson Structures and Their Normal Forms

Poisson Structures and Their Normal Forms by Jean-Paul Dufour
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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.

Birkhäuser Basel; January 2006
335 pages; ISBN 9783764373351
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Title: Poisson Structures and Their Normal Forms
Author: Jean-Paul Dufour; Nguyen Tien Zung
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