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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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Інститут математики НАН України
1991
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| Series: | Український математичний журнал |
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| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/154478 |
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irk-123456789-1544782019-06-16T01:26:41Z Integrability by quadratures for systems of involutive vector fields Basarab-Horwath, P. Статті 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. 1991 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/154478 517.9 en Український математичний журнал Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| topic |
Статті Статті |
| spellingShingle |
Статті Статті Basarab-Horwath, P. Integrability by quadratures for systems of involutive vector fields 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. |
| format |
Article |
| author |
Basarab-Horwath, P. |
| author_facet |
Basarab-Horwath, P. |
| author_sort |
Basarab-Horwath, P. |
| title |
Integrability by quadratures for systems of involutive vector fields |
| title_short |
Integrability by quadratures for systems of involutive vector fields |
| 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_sort |
integrability by quadratures for systems of involutive vector fields |
| publisher |
Інститут математики НАН України |
| publishDate |
1991 |
| topic_facet |
Статті |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154478 |
| 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. |
| series |
Український математичний журнал |
| work_keys_str_mv |
AT basarabhorwathp integrabilitybyquadraturesforsystemsofinvolutivevectorfields |
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2023-05-20T17:43:34Z |
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2023-05-20T17:43:34Z |
| _version_ |
1796153948252405760 |