Lectures on the Geometry of Poisson Manifolds

By:

Izu Vaisman

Format:

Paperback / softback

Series:

Progress in Mathematics

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Description

Everybody having even the slightest interest in analytical mechanics remembers having met there the Poisson bracket of two functions of 2n variables (pi, qi) f g ~(8f8g 8 8 ) (0.1) {f,g} = L...~[ji - [ji~ ,;=1 p, q q p, and the fundamental role it plays in that field. In modern works, this bracket is derived from a symplectic structure, and it appears as one of the main in- gredients of symplectic manifolds. In fact, it can even be taken as the defining clement of the structure (e.g., [TIl]). But, the study of some mechanical sys- tems, particularly systems with symmetry groups or constraints, may lead to more general Poisson brackets. Therefore, it was natural to define a mathematical structure where the notion of a Poisson bracket would be the primary notion of the theory, and, from this viewpoint, such a theory has been developed since the early 19708, by A. Lichnerowicz, A. Weinstein, and many other authors (see the references at the end of the book). But, it has been remarked by Weinstein [We3] that, in fact, the theory can be traced back to S. Lie himself [Lie].

Release date NZ

March 1st, 1994

Author

Izu Vaisman

Audience

Professional & Vocational

Edition

Softcover reprint of the original 1st ed. 1994

Illustrations

VII, 206 p.

Pages

206

Series

Progress in Mathematics

Dimensions

155x235x11

ISBN-13

9783034896498

Product ID

21578084

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