Geodesic
About the whole behavior of trajectories of Darboux systems with cubic
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1463-1484.

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

We study the local and global behavior of trajectories of the differential systems of the form $\dot x= x+P_3(x,y), \dot y=y+Q_3(x,y)$ where $P_3(x,y)$ and $Q_3(x,y)$ are homogeneous cubic polynomials with a common factor.
Keywords: polynomial systems, singular points, Poincaré equator
Mots-clés : phase portraits. 
@article{SEMR_2018_15_a107,
     author = {E. P. Volokitin and V. M. Cheresiz},
     title = {About the whole behavior of trajectories of {Darboux} systems with cubic},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1463--1484},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a107/}
}
TY  - JOUR
AU  - E. P. Volokitin
AU  - V. M. Cheresiz
TI  - About the whole behavior of trajectories of Darboux systems with cubic
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 1463
EP  - 1484
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a107/
LA  - ru
ID  - SEMR_2018_15_a107
ER  - 
%0 Journal Article
%A E. P. Volokitin
%A V. M. Cheresiz
%T About the whole behavior of trajectories of Darboux systems with cubic
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 1463-1484
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a107/
%G ru
%F SEMR_2018_15_a107
E. P. Volokitin; V. M. Cheresiz. About the whole behavior of trajectories of Darboux systems with cubic. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1463-1484. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a107/

[1] A. Bendjeddou, J. Llibre, T. Salhi, “Dynamics of the polynomial differential systems with homogeneous nonlinearities and a star node”, J. Dif. Equ., 254:8 (2013), 3530–3537 | DOI | MR | Zbl

[2] E.P. Volokitin, V.M. Cheresiz, “Qualitative investigation of the planar polynomial Darboux-type systems”, Siberian Electronic Mathematical Reports, 13 (2016), 1170–1186 (Russian. English summary) | MR | Zbl

[3] E.P. Volokitin, V.M. Cheresiz, “Dynamics of the cubic Darboux systems”, Siberian Electronic Mathematical Reports, 14 (2017), 889–902 (Russian. English summary) | MR | Zbl

[4] Differential Equations, 2 (1968), 174–178 | MR | Zbl

[5] Ye Yan Qian, et al., Theory of Limit Cycles, Trans. Math. Monogr., 66, Amer. Math. Soc., Providence, RI, 1986 | MR | Zbl

[6] A. Cima, J. Llibre, “Algebraic and topological classification of the homogeneous cubic vector fields in the plane”, J. Math. Anal. Appl., 147:2 (1990), 420–448 | DOI | MR | Zbl

[7] Springer, Berlin–Heidelberg–New York, 1983 | MR | Zbl | Zbl

[8] F. Dumortier, J. Llibre, J. C. Artés, Qualitative Theory of Planar Differential Systems, Springer, Berlin–Heidelberg–New York, 2006 | MR | Zbl

[9] J. Willey, New York, 1973 | MR | Zbl