%0 Journal Article
%T Normal forms for singularities of one dimensional holomorphic vector fields
%A Antonio Garijo
%A Armengol Gasull
%A Xavier Jarque
%J Electronic Journal of Differential Equations
%D 2004
%I Texas State University
%X : We study the normal form of the ordinary differential equation $dot z=f(z)$, $zinmathbb{C}$, in a neighbourhood of a point $pinmathbb{C}$, 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.
%K Meromorphic vector field
%K holomorphic vector field
%K normal form.
%U http://ejde.math.txstate.edu/Volumes/2004/122/abstr.html