Pfaffian Systems, k-Symplectic Systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2000
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The theory of foliations and contact forms have experienced such great de velopment recently that it is natural they have implications in the field of mechanics. They form part of the framework of what Jean Dieudonne calls "Elie Cartan's great theory ofthe Pfaffian systems", and which even nowa days is still far from being exhausted. The major reference work is. without any doubt that of Elie Cartan on Pfaffian systems with five variables. In it one discovers there the bases of an algebraic classification of these systems, their methods of reduction, and the highlighting ofthe first fundamental in variants. This work opens to us, even today, a colossal field of investigation and the mystery of a ternary form containing the differential invariants of the systems with five variables always deligthts anyone who wishes to find out about them. One of the goals of this memorandum is to present this work of Cartan - which was treated even more analytically by Goursat in its lectures on Pfaffian systems - in order to expound the classifications currently known. The theory offoliations and contact forms appear in the study ofcompletely integrable Pfaffian systems of rank one. In each of these situations there is a local model described either by Frobenius' theorem, or by Darboux' theorem. It is this type of theorem which it would be desirable to have for a non-integrable Pfaffian system which may also be of rank greater than one |
| Physical Description: | 1 Online-Ressource (XIII, 240 p) |
| ISBN: | 9789401595261 9789048154869 |
| DOI: | 10.1007/978-94-015-9526-1 |
Staff View
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| 500 | |a The theory of foliations and contact forms have experienced such great de velopment recently that it is natural they have implications in the field of mechanics. They form part of the framework of what Jean Dieudonne calls "Elie Cartan's great theory ofthe Pfaffian systems", and which even nowa days is still far from being exhausted. The major reference work is. without any doubt that of Elie Cartan on Pfaffian systems with five variables. In it one discovers there the bases of an algebraic classification of these systems, their methods of reduction, and the highlighting ofthe first fundamental in variants. This work opens to us, even today, a colossal field of investigation and the mystery of a ternary form containing the differential invariants of the systems with five variables always deligthts anyone who wishes to find out about them. One of the goals of this memorandum is to present this work of Cartan - which was treated even more analytically by Goursat in its lectures on Pfaffian systems - in order to expound the classifications currently known. The theory offoliations and contact forms appear in the study ofcompletely integrable Pfaffian systems of rank one. In each of these situations there is a local model described either by Frobenius' theorem, or by Darboux' theorem. It is this type of theorem which it would be desirable to have for a non-integrable Pfaffian system which may also be of rank greater than one | ||
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Record in the Search Index
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| id | DE-604.BV042424147 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401595261 9789048154869 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859564 |
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| physical | 1 Online-Ressource (XIII, 240 p) |
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| publisher | Springer Netherlands |
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| spelling | Awane, Azzouz Verfasser aut Pfaffian Systems, k-Symplectic Systems by Azzouz Awane, Michel Goze Dordrecht Springer Netherlands 2000 1 Online-Ressource (XIII, 240 p) txt rdacontent c rdamedia cr rdacarrier The theory of foliations and contact forms have experienced such great de velopment recently that it is natural they have implications in the field of mechanics. They form part of the framework of what Jean Dieudonne calls "Elie Cartan's great theory ofthe Pfaffian systems", and which even nowa days is still far from being exhausted. The major reference work is. without any doubt that of Elie Cartan on Pfaffian systems with five variables. In it one discovers there the bases of an algebraic classification of these systems, their methods of reduction, and the highlighting ofthe first fundamental in variants. This work opens to us, even today, a colossal field of investigation and the mystery of a ternary form containing the differential invariants of the systems with five variables always deligthts anyone who wishes to find out about them. One of the goals of this memorandum is to present this work of Cartan - which was treated even more analytically by Goursat in its lectures on Pfaffian systems - in order to expound the classifications currently known. The theory offoliations and contact forms appear in the study ofcompletely integrable Pfaffian systems of rank one. In each of these situations there is a local model described either by Frobenius' theorem, or by Darboux' theorem. It is this type of theorem which it would be desirable to have for a non-integrable Pfaffian system which may also be of rank greater than one Mathematics Algebra Global differential geometry Differential Geometry Statistical Physics, Dynamical Systems and Complexity Applications of Mathematics Non-associative Rings and Algebras Mathematik Goze, Michel Sonstige oth https://doi.org/10.1007/978-94-015-9526-1 Verlag Volltext |
| spellingShingle | Awane, Azzouz Pfaffian Systems, k-Symplectic Systems Mathematics Algebra Global differential geometry Differential Geometry Statistical Physics, Dynamical Systems and Complexity Applications of Mathematics Non-associative Rings and Algebras Mathematik |
| title | Pfaffian Systems, k-Symplectic Systems |
| title_auth | Pfaffian Systems, k-Symplectic Systems |
| title_exact_search | Pfaffian Systems, k-Symplectic Systems |
| title_full | Pfaffian Systems, k-Symplectic Systems by Azzouz Awane, Michel Goze |
| title_fullStr | Pfaffian Systems, k-Symplectic Systems by Azzouz Awane, Michel Goze |
| title_full_unstemmed | Pfaffian Systems, k-Symplectic Systems by Azzouz Awane, Michel Goze |
| title_short | Pfaffian Systems, k-Symplectic Systems |
| title_sort | pfaffian systems k symplectic systems |
| topic | Mathematics Algebra Global differential geometry Differential Geometry Statistical Physics, Dynamical Systems and Complexity Applications of Mathematics Non-associative Rings and Algebras Mathematik |
| topic_facet | Mathematics Algebra Global differential geometry Differential Geometry Statistical Physics, Dynamical Systems and Complexity Applications of Mathematics Non-associative Rings and Algebras Mathematik |
| url | https://doi.org/10.1007/978-94-015-9526-1 |
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