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math.CV2017
Cheap Complex Limit Cycles
Nataliya Goncharuk, Yury Kudryashov
Consider a holomorphic foliation with singularities of a 2-dimensional complex manifold. In this article we prove a new sufficient condition for this foliation to have countably ma…
math.CV2015★ 1 cited
Bounded limit cycles of polynomial foliations of
Nataliya Goncharuk, Yury Kudryashov
In this article we prove in a new way that a generic polynomial vector field in possesses countably many homologically independent limit cycles. The new proof needs n…
math.CV2014★ 1 cited
Genera of non-algebraic leaves of polynomial foliations of
Nataliya Goncharuk, Yury Kudryashov
In this article, we prove two results. First, we construct a dense subset in the space of polynomial foliations of degree such that each foliation from this subset has a leaf w…