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arXiv · 2306.10706

The cubic Darboux systems with a non-elementary singular point at the Poincar\'{e} equator

Evgenii P. Volokitin
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Abstract

We study the global behavior of the trajectories of the polynomial system $\dot x = x - x^2 y+p x y^2+ y^3, \ \dot y=y+p y^3 , \ \ p\in \mathbb{R}$. Our study is related to the paper {\it Alarcon B., Castro S.B.S.D., Labouriau I.S.} Glodal planar dynamics with star nodes: beyond Hilbert's 16th problem//arXiv:2106/07516v2 [math.DS].

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Evgenii P. Volokitin. 2023-06-19. The cubic Darboux systems with a non-elementary singular point at the Poincar\'{e} equator. https://arxiv.org/abs/2306.10706

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