Том 71
№ 11

Всі номери

Басараб-Норват Р.

Публікацій: 1
Стаття (українською)

Интегрирование в квадратурах инволютивных систем векторных полей

Басараб-Норват Р.

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Укр. мат. журн. - 1991. - 43, № 10. - С. 1330–1337

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.