Integrability by quadratures for systems of involutive vector fields
Starting from results and ideas of S. Lie anb E. Cartan, we give a systematic and geometric treatment of integrability dy quadratures of involutive systems of vector filds, showing how-a-generalization of the usual multiplier can-de constructed with the aid of closed differential forms and enough sy...
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| Published in: | Український математичний журнал |
|---|---|
| Date: | 1991 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
1991
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154478 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Integrability by quadratures for systems of involutive vector fields/ P. Basarab-Horwath // Український математичний журнал. — 1991. — Т. 43, № 10. — С. 1330–1337. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862580854899867648 |
|---|---|
| author | Basarab-Horwath, P. |
| author_facet | Basarab-Horwath, P. |
| citation_txt | Integrability by quadratures for systems of involutive vector fields/ P. Basarab-Horwath // Український математичний журнал. — 1991. — Т. 43, № 10. — С. 1330–1337. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний журнал |
| description | Starting from results and ideas of S. Lie anb E. Cartan, we give a systematic and geometric treatment of integrability dy quadratures of involutive systems of vector filds, showing how-a-generalization of the usual multiplier can-de constructed with the aid of closed differential forms and enough symmetry vector fields. This leads us to explicit formulas for the indepen-. dent integrals. These results allow us to identify symmetries with integral invariants in the sense of Poincare and Cartan. A further (new) result gives the equivalence of integrability by quadratures and the existence of solvable structures, these latter being generalizations. of solvable algebras.
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| first_indexed | 2025-11-26T20:28:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154478 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1027-3190 |
| language | English |
| last_indexed | 2025-11-26T20:28:23Z |
| publishDate | 1991 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Basarab-Horwath, P. 2019-06-15T15:58:37Z 2019-06-15T15:58:37Z 1991 Integrability by quadratures for systems of involutive vector fields/ P. Basarab-Horwath // Український математичний журнал. — 1991. — Т. 43, № 10. — С. 1330–1337. — Бібліогр.: 9 назв. — англ. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/154478 517.9 Starting from results and ideas of S. Lie anb E. Cartan, we give a systematic and geometric treatment of integrability dy quadratures of involutive systems of vector filds, showing how-a-generalization of the usual multiplier can-de constructed with the aid of closed differential forms and enough symmetry vector fields. This leads us to explicit formulas for the indepen-. dent integrals. These results allow us to identify symmetries with integral invariants in the sense of Poincare and Cartan. A further (new) result gives the equivalence of integrability by quadratures and the existence of solvable structures, these latter being generalizations. of solvable algebras. en Інститут математики НАН України Український математичний журнал Статті Integrability by quadratures for systems of involutive vector fields Интегрирование в квадратурах инволютивных систем векторных полей Article published earlier |
| spellingShingle | Integrability by quadratures for systems of involutive vector fields Basarab-Horwath, P. Статті |
| title | Integrability by quadratures for systems of involutive vector fields |
| title_alt | Интегрирование в квадратурах инволютивных систем векторных полей |
| title_full | Integrability by quadratures for systems of involutive vector fields |
| title_fullStr | Integrability by quadratures for systems of involutive vector fields |
| title_full_unstemmed | Integrability by quadratures for systems of involutive vector fields |
| title_short | Integrability by quadratures for systems of involutive vector fields |
| title_sort | integrability by quadratures for systems of involutive vector fields |
| topic | Статті |
| topic_facet | Статті |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154478 |
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