Geodesic
Integrability conditions for a~class of cubic differential systems with a~bundle of two invariant straight lines and one invariant cubic
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2018), pp. 120-138

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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. 
@article{BASM_2018_1_a8,
     author = {Dimitru Cozma and Anatoli Dascalescu},
     title = {Integrability conditions for a~class of cubic differential systems with a~bundle of two invariant straight lines and one invariant cubic},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {120--138},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2018_1_a8/}
}
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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. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2018), pp. 120-138. http://geodesic.mathdoc.fr/item/BASM_2018_1_a8/