Center problem for cubic systems with a~bundle of two invariant straight lines and one invariant conic
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2012), pp. 32-49

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For 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.
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     title = {Center problem for cubic systems with a~bundle of two invariant straight lines and one invariant conic},
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Dumitru Cozma. Center problem for cubic systems with a~bundle of two invariant straight lines and one invariant conic. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2012), pp. 32-49. http://geodesic.mathdoc.fr/item/BASM_2012_1_a3/