4 citations · 7 across the 8 of their papers we have counts for
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Spectra of quadratic vector fields on : The missing relation
Yury Kudryashov, Valente Ramírez
Consider a quadratic vector field on having an invariant line at infinity and isolated singularities only. We define the extended spectra of singularities to be the…
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…
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…
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…