Geodesic
A Generic Analytic Foliation in $\mathbb C^2$ Has Infinitely Many Cylindrical Leaves
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear analytic differential equations, Tome 254 (2006), pp. 192-195 
T. I. Golenishcheva-Kutuzova. A Generic Analytic Foliation in $\mathbb C^2$ Has Infinitely Many Cylindrical Leaves. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear analytic differential equations, Tome 254 (2006), pp. 192-195. http://geodesic.mathdoc.fr/item/TM_2006_254_a7/
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     title = {A~Generic {Analytic} {Foliation} in~$\mathbb C^2$ {Has} {Infinitely} {Many} {Cylindrical} {Leaves}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is well known that a generic polynomial vector field of degree higher than $2$ on the plane has countably many complex limit cycles that are homologically independent on the leaves. In the paper, a similar assertion is proved for analytic vector fields on the complex plane. The proof is based on the results of D. S. Volk and T. S. Firsova.

[1] Ilyashenko Yu., “Centennial history of Hilbert's 16th problem”, Bull. Amer. Math. Soc., 39:3 (2002), 301–354 | DOI | MR | Zbl

[2] Firsova T.S., “Topologiya analiticheskikh sloenii v $\mathbb C^2$. Svoistvo Kupki–Smeila”, Tr. MIAN, 254 (2006), 162–180 | MR

[3] 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

[4] Volk D.S., “Plotnost separatrisnykh svyazok v prostranstve polinomialnykh sloenii v $\mathbb C\mathrm P^2$”, Tr. MIAN, 254 (2006), 181–191 | MR

[5] Chaperon M., “Generic complex flows”, Complex geometry II: Contemporary aspects of mathematics and physics, Hermann, Paris, 2004, 71–79 | MR | Zbl