Details

Poisson Structures and Their Normal Forms

Progress in Mathematics, Band 242

von: Jean-Paul Dufour, Nguyen Tien Zung
128,39 €
Verlag:	Birkhäuser
Format:	PDF
Veröffentl.:	17.01.2006
ISBN/EAN:	9783764373351
Sprache:	englisch
Anzahl Seiten:	336

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Beschreibungen

Titelbeschreibung

<P>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.</P>

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.

Sonderbeitrag

A modern treatment of Poisson geometry Contains results obtained over the past 10 years which are not available in other books Even when it comes to classical results, the book gives new insights Includes supplementary material: sn.pub/extras

Verkaufsargumente

<P>This modern treatment of Poisson geometry fulfills a twofold purpose, offering both a quick, self-contained introduction to Poisson geometry and related subjects, and a comprehensive treatment of the normal form problem in Poisson geometry. Topics covered in detail include singular foliations, Lie groupoids and Lie algebroids. The book includes both new and classic material, offering new insight into results obtained over the past 10 years which are not available in other publications.</P>