Last edited by Malashakar

Wednesday, May 6, 2020 | History

6 edition of **Poisson Structures and Their Normal Forms (Progress in Mathematics)** found in the catalog.

- 389 Want to read
- 1 Currently reading

Published
**October 26, 2005**
by Birkhauser
.

Written in English

- Mathematics,
- Science/Mathematics,
- Geometry - Differential,
- Group Theory,
- Lie theory,
- Mathematics / Group Theory,
- Poisson structure,
- Geometry, Differential,
- Lie algebras,
- Poisson manifolds

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 321 |

ID Numbers | |

Open Library | OL9091014M |

ISBN 10 | 3764373342 |

ISBN 10 | 9783764373344 |

\classi cation" of Poisson structures. There are essentially two types of classi- cations: local and global. In the local case, one is looking for nice local normal forms for Poisson brackets|essentially, coordinate systems in which the Poisson bracket takes on a simple standard form. While these issues will come up from time to time, theyCited by: 3. F. Poisson (auth.): free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books. Poisson Structures and Their Normal Forms. Birkhäuser Basel. A search query can be a title of the book, a name of the author, ISBN or anything else.

Abstract We show how one can handle the formalism developped by Yurii Vorobjev in order to give general results about the problems of linearisation and of normal form of a Poisson structure in the neighborhood of one of its symplectic leaves. Poisson Structures Addeddate Identifier PoissonStructures Identifier-ark ark://tkf2w Ocr ABBYY FineReader (Extended OCR) Ppi Scanner Internet Archive HTML5 Uploader plus-circle Add Review. comment. Reviews There are no reviews yet. Be the first one to write a review. Views. DOWNLOAD OPTIONS.

J.-P. Dufour and N.T. Zung, Poisson Structures and Their Normal Forms, Progress in Mathematics, Vol. , BirkhÃ¤user, Basel, Grading Policy Expository Paper: Students will be encouraged to write (in LaTeX) and present a paper. This is not mandatory. Following the tradition of topics courses, there will be no. The program for Poisson was remarkable for the overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction.

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Buy Poisson Structures and Their Normal Forms (Progress in Mathematics) on FREE SHIPPING on qualified orders Poisson Structures and Their Normal Forms (Progress in Mathematics): Dufour, Jean-Paul, Zung, Nguyen Tien: : BooksCited by: 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. “Poisson structures and their normal forms”, Progress in Mathematics, V olumeBirkhauser, The aim of these notes is to give an introduction to Poisson.

Home» MAA Publications» MAA Reviews» Poisson Structures and Their Normal Forms Poisson Structures and Their Normal Forms Jean-Paul Dufour and Nguyen Tien Zung.

Poisson structures and their normal forms. [Jean-Paul Dufour; Nguyen Tien Zung] The aim of this book is twofold.

On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. Multiplicative and quadratic poisson structures Nambu structures and singular foliations Lie groupoids Book Title:Poisson Structures and Their Normal Forms (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". Poisson Structures and their Normal Forms Jean-Paul Dufour and Nguyen Tien Zung These notes are based on some sections of our book,“Poisson structures and their normal form”, Progress in Mathematics, Vol.

Birkh¨auser, to appear this year. In turn, our lectures will be based on some parts of these notes. J i. Get this from a library. Poisson structures and their normal forms. [Jean-Paul Dufour; Nguyen Tien Zung] -- Presents a treatment of Poisson geometry fulfilling a twofold purpose, offering both a quick, self-contained introduction to Poisson geometry and related subjects, and a comprehensive treatment of.

Normal forms of Poisson structures JEAN-PAUL DUFOUR NGUYEN TIEN ZUNG These notes arise from a minicourse given by the two authors at the Summer School on Poisson Geometry, ICTP, The main reference is our recent monograph “Poisson structures and their normal forms”, Progress in Mathematics, VolumeBirkhauser, Singular symplectic foliations and transverse Poisson structures 12 The Schouten bracket 14 Vorobjev geometric data and transversal structures 19 Chapter 2.

Poisson cohomology 23 Poisson cohomology 23 Normal forms of Poisson structures 26 Cohomology of Lie algebras 29 The curl operator 32 Chapter Size: KB. Author: Dufour, Jean-Paul et al.; Genre: Book; Published in Print: ; Title: Poisson structures and their normal formsCited by: In geometry, a Poisson structure on a smooth manifold is a Lie bracket {⋅, ⋅} (called a Poisson bracket in this special case) on the algebra ∞ of smooth functions on, subject to the Leibniz rule {,} = {,} + {,}.Said in another manner, it is a Lie algebra structure on the vector space of smooth functions on such that = {, ⋅}: ∞ → ∞ is a vector field for each smooth function.

Abstract. After studying linearization and normal forms for Poisson structures with a non-trivial linear part in the previous two chapters, it is a logical next step to talk about Poisson structures which begin with a.

Normal forms for locally exact Poisson structures in R 3. In this section, we assume that the origin is not only singular but also a zero rank point for the locally exact Poisson structure P Ψ.

In such a case the function Ψ has a critical point at the origin. The generic caseCited by: 4. YVONNE CHOQUET-BRUHAT, CÉCILE DEWITT-MORETTE, in Analysis, Manifolds and Physics, 0 DEFINITIONS. Poisson structures are interesting in connection with the hamiltonian formulation of classical physical systems and their quantization.

Let M be a C ∞ manifold of dimension m. Let C ∞ (M, ℝ) be the space of C ∞ real valued functions on M. A Poisson structure on M is a mapping called. Buy Poisson Structures and Their Normal Forms (Progress in Mathematics) by Jean-Paul Dufour, Nguyen Tien Zung (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible orders. In this chapter we give a few basic, general constructions which allow one to build new Poisson structures from given ones.

These constructions are fundamental and will be used throughout the book. Poisson Book () By NTZung, on January 2nd, Jean-Paul Dufour and Nguyen Tien Zung, Poisson structures and their normal forms, Progress in Mathematics, Vol. Birkhäuser Verlag, Basel, xvi+ pp. The book has been reviewed by Jan Sanders (University of Amsterdam) for LMS.

A really nice book is. Poisson-Geometrie und Deformationsquantisierung: Eine Einführung (S. Waldmann). It is a shame there is not an english translation.

You could also check: Lectures on the geometry of Poisson Manifolds (Izu Vaisman) and for the connection with Lie groupoids/algebroids see: Poisson structures and their normal forms (Jean.

The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson : Hardcover. Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory.

In each one of these contexts, it turns out that the Poisson structure is not a theoretical.The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.

Poisson structures naturally appear in very different forms and contexts [with s]ymplectic manifolds, Lie algebras, singularity theory, r-matrices all lead[ing] to a certain type of Poisson structure, sharing several features despite the distances between the mathematics they originate from.