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

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.

31 pages, 11 figures. arXiv admin note: text overlap with arXiv:1601.07767 by other authors