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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2006, номер 3, страницы 3–16
(Mi basm104)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Lie algebras of operators and invariant $GL(2,\mathbb{R})$-integrals for Darboux type differential systems
O. V. Diaconescu, M. N. Popa Institute of Mathematics and Computer Sciences,
Academy of Sciences of Moldova, Chisinau, Moldova
Аннотация:
In this article two-dimensional autonomous Darboux type differential systems with nonlinearities of the $i^{th} (i=\overline{2,7})$ degree with respect to the phase variables are considered. For every such system the admitted Lie algebra is constructed. With the aid of these algebras particular invariant $GL(2,\mathbb{R})$-integrals as well as first integrals of considered systems are constructed. These integrals represent the algebraic curves of the $(i-1)^{th}(i=\overline{2,7})$ degree. It is showed that the Darboux type systems with nonlinearities of the $2^{nd}$, the $4^{th}$ and the $6^{th}$ degree with respect to the phase variables do not have limit cycles.
Ключевые слова и фразы:
Darboux type differential system, comitant, invariant $GL(2,\mathbb{R})$-integrating factor, invariant $GL(2,\mathbb{R})$-integral, limit cycle.
Поступила в редакцию: 21.08.2006
Образец цитирования:
O. V. Diaconescu, M. N. Popa, “Lie algebras of operators and invariant $GL(2,\mathbb{R})$-integrals for Darboux type differential systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2006, no. 3, 3–16
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm104 https://www.mathnet.ru/rus/basm/y2006/i3/p3
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Страница аннотации: | 316 | PDF полного текста: | 100 | Список литературы: | 46 | Первая страница: | 1 |
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