Garijo, AntonioGasull, ArmengolJarque, Xavier2021-05-142021-05-142004-10-15Garijo, A., Gasull, A., & Jarque, X. (2004). Normal forms for singularities of one dimensional holomorphic vector fields. <i>Electronic Journal of Differential Equations, 2004</i>(122), pp. 1-7.1072-6691https://hdl.handle.net/10877/13543We study the normal form of the ordinary differential equation ż = ƒ(z), z ∈ ℂ, in a neighbourhood of a point p ∈ ℂ, where ƒ 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.Text7 pages1 file (.pdf)enAttribution 4.0 InternationalMeromorphic vector fieldHolomorphic vector fieldNormal formArticle