Lectures on the Geometry of Poisson Manifolds (Paperback) (ISBN-13: 9783034896498)

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].

Author: Izu Vaisman
ISBN-10: 3034896492
ISBN-13: 9783034896498
Publisher: Birkhauser
Language: English
Published: 10/23/2012
Pages: 206
Format: Paperback
Weight: 0.69lbs
Size: 9.21h x 6.14w x 0.46d