Poisson Structures and Their Normal Forms

• Main Authors: Dufour, Jean-Paul (Author), Zung, Nguyen Tien (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Bass, H. (Editor), Oesterlé, J. (Editor), Weinstein, A. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2005.
• Series: Progress in Mathematics ; 242
• Subjects: Mathematics.; Topological groups.; Lie groups.; Topological Groups, Lie Groups.

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...

Table of Contents:

• Generalities on Poisson Structures
• Poisson Cohomology
• Levi Decomposition
• Linearization of Poisson Structures
• Multiplicative and Quadratic Poisson Structures
• Nambu Structures and Singular Foliations
• Lie Groupoids
• Lie Algebroids.