Geodesic
The Density of Separatrix Connections in the Space of Polynomial Foliations in~$\mathbb C\mathrm P^2$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear analytic differential equations, Tome 254 (2006), pp. 181-191.

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A complex analog of the Hayashi connecting lemma is proved; namely, in the space of polynomial vector fields of degree higher than $1$ on the complex plane, the vector fields that have a common complex separatrix of two singular points are dense. 
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D. S. Volk. The Density of Separatrix Connections in the Space of Polynomial Foliations in~$\mathbb C\mathrm P^2$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear analytic differential equations, Tome 254 (2006), pp. 181-191. http://geodesic.mathdoc.fr/item/TM_2006_254_a6/

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