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arXiv · 1810.09396

On first integrals admitting asymptotic expansion for holomorphic foliations in dimension two

F. Reis
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Abstract

In this paper we study the dynamics of a holomorphic vector field near a singular point in dimension two using asymptotic expansion techniques. We consider a holomorphic vector field admitting first integrals in small sectors with nonzero asymptotic expansion. Under some natural hypotheses we prove the existence of a holomorphic first integral.

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F. Reis. 2018-10-22. On first integrals admitting asymptotic expansion for holomorphic foliations in dimension two. https://arxiv.org/abs/1810.09396

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