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