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 
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/
@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},
     pages = {181--191},
     year = {2006},
     volume = {254},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a6/}
}
TY  - JOUR
AU  - D. S. Volk
TI  - The Density of Separatrix Connections in the Space of Polynomial Foliations in $\mathbb C\mathrm P^2$
JO  - Informatics and Automation
PY  - 2006
SP  - 181
EP  - 191
VL  - 254
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a6/
LA  - ru
ID  - TRSPY_2006_254_a6
ER  - 
%0 Journal Article
%A D. S. Volk
%T The Density of Separatrix Connections in the Space of Polynomial Foliations in $\mathbb C\mathrm P^2$
%J Informatics and Automation
%D 2006
%P 181-191
%V 254
%U http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a6/
%G ru
%F TRSPY_2006_254_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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