Poisson Structures and Their Normal Forms

  • Jean-Paul Dufour
  • Nguyen Tien Zung
  • Editors
  • H. Bass
  • J. Oesterlé
  • A. Weinstein

Part of the Progress in Mathematics book series (PM, volume 242)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Pages 39-75
  3. Pages 77-104
  4. Pages 203-234
  5. Pages 235-262
  6. Back Matter
    Pages 263-321

About this book

Introduction

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.

Keywords

Lie Lie theory Manifold Poisson structure cohomology geometry homology

Authors and affiliations

  • Jean-Paul Dufour
    • 1
  • Nguyen Tien Zung
    • 2
  1. 1.Département de mathématiqueUniversité de MontpellierMontpellierFrance
  2. 2.Laboratoire Émile Picard, UMR 5580 CNRSInstitut de Mathématiques Université Paul SabatierToulouseFrance

Bibliographic information

  • DOI https://doi.org/10.1007/b137493
  • Copyright Information Birkhäuser Verlag 2005
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-7334-4
  • Online ISBN 978-3-7643-7335-1
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book