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Regular version of the site

Article

Bounded limit cycles of polynomial foliations of ℂ²

Kudryashov Y., Goncharuk N. B.

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.