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Poisson Structures and Their Normal Forms [electronic resource] / by Jean-Paul Dufour, Nguyen Tien Zung ; edited by H. Bass, J. Oesterlé, A. Weinstein.

By: Dufour, Jean-Paul [author.].
Contributor(s): Zung, Nguyen Tien [author.] | Bass, H [editor.] | Oesterlé, J [editor.] | Weinstein, A [editor.] | SpringerLink (Online service).
Material type: TextTextSeries: Progress in Mathematics: 242Publisher: Basel : Birkhäuser Basel, 2005Description: XV, 321 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783764373351.Subject(s): Topological Groups | Topological Groups, Lie GroupsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 512.55 | 512.482 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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Poisson structures and their normal forms by Dufour Jean-Paul
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