Lectures on the Geometry of Poisson Manifolds (Progress in Mathematics, 118, Band 118) - Hardcover

Vaisman, Izu

Hardcover

ISBN 10: 3764350164 ISBN 13: 9783764350161

Verlag: Birkhäuser Verlag, 1994

Inhaltsangabe

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].

Details zur Ausgabe

• Verlag: Birkhäuser Verlag
• Erscheinungsdatum: 1994
• Sprache: Englisch
• ISBN 10: 3764350164
• ISBN 13: 9783764350161
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 213
• Kontakt zum Hersteller: Springer-Verlag GmbH; customerservice@springernature.com; ; Tiergartenstraße 17; Heidelberg; Baden-Württemberg; 69121; Deutschland