Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, Number 1, Pages 120–138 (Mi basm470)  
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
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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
Document Type: Article
MSC: 34C05
Language: English
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
Citation in format AMSBIB
\Bibitem{CozDas18}
\by Dimitru~Cozma, Anatoli~Dascalescu
\paper Integrability conditions for a~class of cubic differential systems with a~bundle of two invariant straight lines and one invariant cubic
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2018
\issue 1
\pages 120--138
\mathnet{http://mi.mathnet.ru/basm470}
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    • This publication is cited in the following 1 articles:
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    		Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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