Poisson Structures and Their Normal Forms

2005
ISBN: 978-3-7643-7334-4
Verlag: Springer

Buch, Englisch, Band 242, 324 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 682 g

Reihe: Progress in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Zung, Nguyen Tien

Dufour, Jean-Paul

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

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.