A Generic Analytic Foliation in $\mathbb C^2$ Has Infinitely Many Cylindrical Leaves

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.