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// Mathematical notes of NEFU
// Archive
Mathematical notes of NEFU,
2023
Volume 30,
Issue 3,
Pages
27–37
(Mi svfu390)
Mathematics
Cubic Darboux systems with a non-elementary singular point at the Poincare equator
E. P. Volokitin
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
We study the global behavior of the trajectories of the polynomial system
$x = x - x^2y + pxy^2 + y^3, y = y + py^3$
,
$p \in R$
. Our study is related to the paper arXiv:
2106/07516v2 [math.DS]
.
Keywords:
polynomial systems, singular points, Poincare equator, phase portraits, rational integrals.
UDC:
517.925
Received:
13.06.2023
Accepted:
04.09.2023
DOI:
10.25587/SVFU.2023.68.43.004
Fulltext:
PDF file (267 kB)
©
Steklov Math. Inst. of RAS
, 2024