Analytical classification of saddle-node vector fields

We describe the classification of germs of holomorphic saddle-node vector fields <f>Z</f> at <f>(0,0)∈C2</f>, up to analytical change of local coordinates. The classification of saddle-node foliations <f>FZ</f>, obtained by Martinet and Ramis, led to functional moduli. We reduce the conjugacy equation between two vector fields inducing the same foliation to a homological equation. We derive then a complete set of additional functional invariants for vector fields. To cite this article: L. Teyssier, C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright &y& Elsevier]