Geodesic
The Density of Separatrix Connections in the Space of Polynomial Foliations in~$\mathbb C\mathrm P^2$
Informatics and Automation, 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. 
@article{TRSPY_2006_254_a6,
     author = {D. S. Volk},
     title = {The {Density} of {Separatrix} {Connections} in the {Space} of {Polynomial} {Foliations} in~$\mathbb C\mathrm P^2$},
     journal = {Informatics and Automation},
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     volume = {254},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a6/}
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D. S. Volk. The Density of Separatrix Connections in the Space of Polynomial Foliations in~$\mathbb C\mathrm P^2$. Informatics and Automation, Nonlinear analytic differential equations, Tome 254 (2006), pp. 181-191. http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a6/