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Lectures on the Geometry of Poisson Manifolds (Paperback, Softcover reprint of the original 1st ed. 1994)
Loot Price: R1,533
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Lectures on the Geometry of Poisson Manifolds (Paperback, Softcover reprint of the original 1st ed. 1994)
Series: Progress in Mathematics, 118
Expected to ship within 10 - 15 working days
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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].
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