Versal deformation of the analytic saddle-node

Frank Loray (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We derive simple formsfor saddle-node singular points of analytic foliations in the real or complex plane just by gluing foliated complex manifolds. We give the versal analytic deformation of the simplest model.We also derive a unique analytic form for those saddle-node having a central manifold.By this way, we recover and generalize results earlier proved by J. Ecalle by using mould theoryand partially answer to some questions asked byJ. Martinet and J.-P. Ramis in the 80's.

Mots clés: Foliations; singularities; saddle-nodes; normal forms

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]

Frank Loray. Versal deformation of the analytic saddle-node. Analyse complexe, Systèmes dynamiques, Sommabilité des séries divergentes et Théories Galoisiennes, Volume en l'honneur de Jean-Pierre Ramis, 2004, Toulouse, France. pp.167--187. ⟨hal-00001192⟩