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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, Number 1, Pages 120–138
(Mi basm470)
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This article is cited in 1 scientific paper (total in 1 paper)
Integrability conditions for a class of cubic differential systems with a bundle of two invariant straight lines and one invariant cubic
Dimitru Cozmaa, Anatoli Dascalescub a Department of Mathematics, Tiraspol State University, 5 Gh. Iablocichin str., Chişinău, MD2069, Republic of Moldova
b Institute of Mathematics and Computer Science, 5 Academiei str., Chişinău, MD2028, Republic of Moldova
Abstract:
We determine conditions for the origin to be a center for a class of cubic differential systems having a bundle of two invariant straight lines and one invariant cubic. We prove that a fine focus $O(0,0)$ is a center if and only if the first three Lyapunov quantities vanish.
Keywords and phrases:
cubic differential system, center-focus problem, invariant algebraic curve, integrability.
Received: 26.03.2018
Citation:
Dimitru Cozma, Anatoli Dascalescu, “Integrability conditions for a class of cubic differential systems with a bundle of two invariant straight lines and one invariant cubic”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 1, 120–138
Linking options:
https://www.mathnet.ru/eng/basm470 https://www.mathnet.ru/eng/basm/y2018/i1/p120
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Abstract page: | 148 | Full-text PDF : | 40 | References: | 13 |
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