TY - JOUR
T1 - On codimension one foliations with prescribed cuspidal separatrix
AU - Fernández-Sánchez, Percy
AU - Mozo-Fernández, Jorge
AU - Neciosup, Hernán
PY - 2014/2/15
Y1 - 2014/2/15
N2 - In this paper, we will construct a pre-normal form for germs of codimension one holomorphic foliation having a particular type of separatrix, of cuspidal type. As an application, we will explain how this form could be used in order to study the analytic classification of the singularities via the projective holonomy, in the generalized surface case. We will also give an application to the analytic classification of singularities, and a sufficient condition, in the quasi-homogeneous, three-dimensional case, for these foliations to be of generalized surface type.
AB - In this paper, we will construct a pre-normal form for germs of codimension one holomorphic foliation having a particular type of separatrix, of cuspidal type. As an application, we will explain how this form could be used in order to study the analytic classification of the singularities via the projective holonomy, in the generalized surface case. We will also give an application to the analytic classification of singularities, and a sufficient condition, in the quasi-homogeneous, three-dimensional case, for these foliations to be of generalized surface type.
UR - http://www.scopus.com/inward/record.url?scp=84890863134&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2013.12.002
DO - 10.1016/j.jde.2013.12.002
M3 - Article
AN - SCOPUS:84890863134
SN - 0022-0396
VL - 256
SP - 1702
EP - 1717
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 4
ER -