Geodesic
Center problem for a~class of cubic systems with a~bundle of two invariant straight lines and one invariant conic
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2010), pp. 51-66

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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. 
@article{BASM_2010_3_a6,
     author = {Dimitru Cozma},
     title = {Center problem for a~class of cubic systems with a~bundle of two invariant straight lines and one invariant conic},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {51--66},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2010_3_a6/}
}
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Dimitru Cozma. Center problem for a~class of cubic systems with a~bundle of two invariant straight lines and one invariant conic. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2010), pp. 51-66. http://geodesic.mathdoc.fr/item/BASM_2010_3_a6/