Geodesic
The Lyapunov quantities and the center conditions for a~class of bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2017), pp. 112-130

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For the autonomous bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree the $GL(2,\mathbb R)$-invariant recurrence equations for determination of the Lyapunov quantities were established. Moreover, the general form of Lyapunov quantities for the mentioned systems is obtained. For a class of such systems the necessary and sufficient $GL(2,\mathbb R)$-invariant conditions for the existence of center are given. 
@article{BASM_2017_2_a8,
     author = {Iurie Calin and Stanislav Ciubotaru},
     title = {The {Lyapunov} quantities and the center conditions for a~class of bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {112--130},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2017_2_a8/}
}
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Iurie Calin; Stanislav Ciubotaru. The Lyapunov quantities and the center conditions for a~class of bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2017), pp. 112-130. http://geodesic.mathdoc.fr/item/BASM_2017_2_a8/