Analytical and formal classifications of quasi-homogeneous foliations in C^2

We prove a result of classification for germs of formal and convergent quasi-homogeneous foliations in C 2 with fixed separatrix. Basically, we prove that the analytical and formal class of such a foliation depend respectively only on the analytical and formal class of its representation of projecti...

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Bibliographic Details
Published in:Journal of Differential Equations 2008, Vol.245 (6), p.1656-1680
Main Author: Genzmer, Yohann
Format: Article
Language:English
Subjects:
Complex Variables
Dynamical Systems
Mathematics
Online Access:Get full text
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Summary:We prove a result of classification for germs of formal and convergent quasi-homogeneous foliations in C 2 with fixed separatrix. Basically, we prove that the analytical and formal class of such a foliation depend respectively only on the analytical and formal class of its representation of projective holonomy.
ISSN:0022-0396
1090-2732