English

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

Dynamical Systems 2018-10-23 v1

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.

Keywords

Cite

@article{arxiv.1810.09396,
  title  = {On first integrals admitting asymptotic expansion for holomorphic foliations in dimension two},
  author = {F. Reis},
  journal= {arXiv preprint arXiv:1810.09396},
  year   = {2018}
}

Comments

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