Geodesic
Algebraic ovals and rational integrals of Darboux-type systems
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1108-1124

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the question of the existence of algebraic solutions, polynomial and rational integrals for systems of ordinary differential equations of the form $\dot x=x+P_n(x,y),\ \dot y=y+Q_n(x,y)$, where $P_n(x,y), $ $Q_n(x,y)$ are homogeneous polynomials of $n$th degree.
Keywords: polynomial systems, rational integrals
Mots-clés : algebraic limit cycles, non-algebraic limit cycles, phase portraits. 
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     author = {E. P. Volokitin and V. M. Cheresiz},
     title = {Algebraic ovals and rational integrals of {Darboux-type} systems},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1108--1124},
     publisher = {mathdoc},
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     number = {2},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a47/}
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E. P. Volokitin; V. M. Cheresiz. Algebraic ovals and rational integrals of Darboux-type systems. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1108-1124. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a47/