Bounded limit cycles of polynomial foliations of $\mathbb CP^2$

Nataliya Goncharuk; Yury Kudryashov

doi:10.1007/s00574-016-0005-9

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arXiv · 1504.03313

Bounded limit cycles of polynomial foliations of $\mathbb CP^2$

Nataliya Goncharuk·Yury Kudryashov

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Abstract

In this article we prove in a new way that a generic polynomial vector field in $\mathbb C^2$ 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.

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Nataliya Goncharuk, Yury Kudryashov. 2015-04-13. Bounded limit cycles of polynomial foliations of $\mathbb CP^2$. https://doi.org/10.1007/s00574-016-0005-9

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