Lectures on the Geometry of Poisson Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1994
|
| Schriftenreihe: | Progress in Mathematics
118 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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] |
| Beschreibung: | 1 Online-Ressource (VII, 206 p) |
| ISBN: | 9783034884952 9783034896498 |
| DOI: | 10.1007/978-3-0348-8495-2 |
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Datensatz im Suchindex
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| author | Vaisman, Izu |
| author_facet | Vaisman, Izu |
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| building | Verbundindex |
| bvnumber | BV042422140 |
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| ctrlnum | (OCoLC)879624686 (DE-599)BVBBV042422140 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8495-2 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034884952 9783034896498 |
| language | English |
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| physical | 1 Online-Ressource (VII, 206 p) |
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| publishDate | 1994 |
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| publisher | Birkhäuser Basel |
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| series2 | Progress in Mathematics |
| spelling | Vaisman, Izu Verfasser aut Lectures on the Geometry of Poisson Manifolds by Izu Vaisman Basel Birkhäuser Basel 1994 1 Online-Ressource (VII, 206 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 118 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] Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Theoretical, Mathematical and Computational Physics Mathematik Poisson-Mannigfaltigkeit (DE-588)4231918-3 gnd rswk-swf Poisson-Mannigfaltigkeit (DE-588)4231918-3 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-8495-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Vaisman, Izu Lectures on the Geometry of Poisson Manifolds Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Theoretical, Mathematical and Computational Physics Mathematik Poisson-Mannigfaltigkeit (DE-588)4231918-3 gnd |
| subject_GND | (DE-588)4231918-3 |
| title | Lectures on the Geometry of Poisson Manifolds |
| title_auth | Lectures on the Geometry of Poisson Manifolds |
| title_exact_search | Lectures on the Geometry of Poisson Manifolds |
| title_full | Lectures on the Geometry of Poisson Manifolds by Izu Vaisman |
| title_fullStr | Lectures on the Geometry of Poisson Manifolds by Izu Vaisman |
| title_full_unstemmed | Lectures on the Geometry of Poisson Manifolds by Izu Vaisman |
| title_short | Lectures on the Geometry of Poisson Manifolds |
| title_sort | lectures on the geometry of poisson manifolds |
| topic | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Theoretical, Mathematical and Computational Physics Mathematik Poisson-Mannigfaltigkeit (DE-588)4231918-3 gnd |
| topic_facet | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Theoretical, Mathematical and Computational Physics Mathematik Poisson-Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-3-0348-8495-2 |
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