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IMI/Publicaţii/BASM/Ediţii/BASM n.1(86), 2018/

Integrability conditions for a class of cubic differential systems with a bundle of two invariant straight lines and one invariant cubic

Authors: Dumitru Cozma, Anatoli Dascalescu

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.

Dumitru Cozma
Department of Mathematics
Tiraspol State University
5 Gh. Iablocichin str., Chisinau
MD2069, Republic of Moldova
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Anatoli Dascalescu
Institute of Mathematics and Computer Science
5 Academiei str., Chisinau
MD2028, Republic of Moldova
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