Geodesic
A~Generic Analytic Foliation in~$\mathbb C^2$ Has Infinitely Many Cylindrical Leaves
Informatics and Automation, Nonlinear analytic differential equations, Tome 254 (2006), pp. 192-195

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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. 
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     author = {T. I. Golenishcheva-Kutuzova},
     title = {A~Generic {Analytic} {Foliation} in~$\mathbb C^2$ {Has} {Infinitely} {Many} {Cylindrical} {Leaves}},
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     publisher = {mathdoc},
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T. I. Golenishcheva-Kutuzova. A~Generic Analytic Foliation in~$\mathbb C^2$ Has Infinitely Many Cylindrical Leaves. Informatics and Automation, Nonlinear analytic differential equations, Tome 254 (2006), pp. 192-195. http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a7/