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. 
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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/

[1] Ilyashenko Yu.S., “Topologiya fazovykh portretov analiticheskikh differentsialnykh uravnenii na kompleksnoi proektivnoi ploskosti”, Tr. sem. im. I.G. Petrovskogo, 4 (1978), 83–136 | MR | Zbl

[2] Khudai-Verenov M.G., “Ob odnom svoistve reshenii odnogo differentsialnogo uravneniya”, Mat. sb., 56:3 (1962), 301–308 | MR | Zbl

[3] Scherbakov A.A., “O plotnosti orbity psevdogruppy konformnykh otobrazhenii i obobschenii teoremy Khudai-Verenova”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 1982, no. 4, 10–15 | Zbl

[4] Nakai I., “Separatrices for non-solvable dynamics on $\mathbb C,0$”, Ann. Inst. Fourier, 44:2 (1994), 569–599 | MR | Zbl

[5] Milnor Dzh., Golomorfnaya dinamika, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2000

[6] Pyartli A.S., “Kvadratichnye vektornye polya na $\mathbb C\mathrm P^2$ s razreshimoi gruppoi monodromii na beskonechnosti”, Tr. MIAN, 254 (2006), 130–161 | MR

[7] Pyartli A.S., “Ratsionalnye differentsialnye uravneniya s kommutativnoi gruppoi monodromii na beskonechnosti”, Tr. Mosk. mat. o-va, 61 (2000), 75–106 | MR | Zbl