Normal forms for singularities of one dimensional holomorphic vector fields

Antonio Garijo, Armengol Gasull, Xavier Jarque

Research output: Contribution to journalArticleResearchpeer-review

14 Citations (Scopus)

Abstract

We study the normal form of the ordinary differential equation ż = f(z), z ∈ ℂ, in a neighbourhood of a point p ∈ ℂ, where f is a one-dimensional holomorphic function in a punctured neighbourhood of p. Our results include all cases except when p is an essential singularity. We treat all the other situations, namely when p is a regular point, a pole or a zero of order n. Our approach is based on a formula that uses the flow associated with the differential equation to search for the change of variables that gives the normal form.
Original languageEnglish
Pages (from-to)1-7
JournalElectronic Journal of Differential Equations
Volume2004
Publication statusPublished - 15 Oct 2004

Keywords

  • Holomorphic vector field
  • Meromorphic vector field
  • Normal form

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