The cubic Darboux systems with a non-elementary singular point at the Poincar\'e equator
Abstract
We study the global behavior of the trajectories of the polynomial system x = x - x2 y+p x y2+ y3, \ y=y+p y3 , \ \ p∈ R. Our study is related to the paper 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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