Normal forms for singularities of one dimensional holomorphic vector fields
Date
2004-10-15
Authors
Garijo, Antonio
Gasull, Armengol
Jarque, Xavier
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We 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.
Description
Keywords
Meromorphic vector field, Holomorphic vector field, Normal form
Citation
Garijo, 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.
Rights
Attribution 4.0 International