Poisson Structures and Their Normal Forms
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.

1012710577
Poisson Structures and Their Normal Forms
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.

139.99 In Stock
Poisson Structures and Their Normal Forms

Poisson Structures and Their Normal Forms

Poisson Structures and Their Normal Forms

Poisson Structures and Their Normal Forms

Hardcover(2005)

$139.99 
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Overview

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.


Product Details

ISBN-13: 9783764373344
Publisher: Birkhäuser Basel
Publication date: 10/26/2005
Series: Progress in Mathematics , #242
Edition description: 2005
Pages: 324
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

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.
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