TY - JOUR
T1 - Normal forms for singularities of one dimensional holomorphic vector fields
AU - Garijo, Antonio
AU - Gasull, Armengol
AU - Jarque, Xavier
PY - 2004/10/15
Y1 - 2004/10/15
N2 - 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.
AB - 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.
KW - Holomorphic vector field
KW - Meromorphic vector field
KW - Normal form
UR - https://www.scopus.com/pages/publications/8744261998
M3 - Article
SN - 1072-6691
VL - 2004
SP - 1
EP - 7
JO - Electronic Journal of Differential Equations
JF - Electronic Journal of Differential Equations
ER -