Geodesic
Normal forms for singularities of one dimensional holomorphic vector fields
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the normal form of the ordinary differential equation $\dot z=f(z), z\in\mathbb{C}$, in a neighbourhood of a point $p\in\mathbb{C}$, 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.
Classification : 34C20, 34A34, 32A10, 37C10
Keywords: meromorphic vector field, holomorphic vector field, normal form 
@article{EJDE_2004__2004__a33,
     author = {Garijo, Antonio and Gasull, Armengol and Jarque, Xavier},
     title = {Normal forms for singularities of one dimensional holomorphic vector fields},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a33/}
}
TY  - JOUR
AU  - Garijo, Antonio
AU  - Gasull, Armengol
AU  - Jarque, Xavier
TI  - Normal forms for singularities of one dimensional holomorphic vector fields
JO  - Electronic Journal of Differential Equations
PY  - 2004
VL  - 2004
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a33/
LA  - en
ID  - EJDE_2004__2004__a33
ER  - 
%0 Journal Article
%A Garijo, Antonio
%A Gasull, Armengol
%A Jarque, Xavier
%T Normal forms for singularities of one dimensional holomorphic vector fields
%J Electronic Journal of Differential Equations
%D 2004
%V 2004
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a33/
%G en
%F EJDE_2004__2004__a33
Garijo, Antonio; Gasull, Armengol; Jarque, Xavier. Normal forms for singularities of one dimensional holomorphic vector fields. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a33/