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Conference Papers Year : 2004

Versal deformation of the analytic saddle-node

Frank Loray


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.
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hal-00001192 , version 1 (03-03-2004)



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⟩
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