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Working paper

Bounded limit cycles of polynomial foliations of ℂP²

arxiv.org. math. Cornell University, 2015. No. 1504.03313.
Goncharuk N. B., Kudryashov Y.
In this article we prove in a new way that a generic polynomial vector field in ℂ² possesses countably many homologically independent limit cycles. The new proof needs no estimates on integrals, provides thinner exceptional set for quadratic vector fields, and provides limit cycles that stay in a bounded domain.