Generalization of Jacobi’s Theorem on the Last Multiplier

Авторы: Kugushev E.I., Salnikova T.V.
Журнал: Doklady Mathematics
Том: 109
Год издания: 2024
Издательство: Maik Nauka/Interperiodica Publishing
Местоположение издательства: Russian Federation
Первая страница: 282
Последняя страница: 286
DOI: 10.1134/S1064562424702144
Аннотация: To satisfy the conditions of Jacobi’s theorem on the last multiplier, the existence of an invariantmeasure and a sufficient number of independent first integrals are needed. In this case, the system can belocally integrated by quadratures. There are examples of systems for which the existence of partial first integrals is sufficient for the possibility of integration by quadratures. Moreover, integration by quadraturesoccurs at the level of partial first integrals. In this paper, Jacobi’s theorem on the last multiplier is extendedto the general situation when the first integrals include partial ones.
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