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Research articles

Center problem for a class of cubic systems with a bundle of two invariant straight lines and one invariant conic

Dimitru Cozma

Department of Mathematics, Tiraspol State University, Chişinău, Moldova

Abstract: For a class of cubic differential systems with a bundle of two invariant straight lines and one invariant conic it is proved that a weak focus is a center if and only if the first four Liapunov quantities $L_j$, $j=\overline{1,4}$, vanish.

Keywords and phrases: cubic differential system, center-focus problem, invariant algebraic curve, integrability.

MSC: 34C05

Received: 15.06.2010

Language: English

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