arXiv 1504.033132015-04-13math.CVmath.DS

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

Nataliya Goncharuk, Yury Kudryashov

发表信息：: Bulletin of the Brazilian Mathematical Society, New Series 48:1, 2017, pp. 63-83
DOI：: 10.1007/s00574-016-0005-9

英文摘要：

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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