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Integrability by quadratures for systems of involutive vector fields

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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Bibliographic Details
Main Author: Basarab-Horwath, P.
Format: Article
Language:English
Published: Інститут математики НАН України 1991
Series:Український математичний журнал
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Online Access:http://dspace.nbuv.gov.ua/handle/123456789/154478
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Summary: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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