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

2018/10/22 by Reis, F.
#32S65 #57R30 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F75 #Secondary 32M25

paper · doi:10.48550/arxiv.1810.09396

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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