Versal deformation of the analytic saddle-node

Details Versal deformation of the analytic saddle-node Versal deformation of the analytic saddle-node

2004-03-03

arxiv.org/abs/math/0403079v1

Analyse complexe, Syst\`emes dynamiques, Sommabilit\'e des s\'eries divergentes et Th\'eories Galoisiennes (2004) 167--187

Mathematics

Differential Geometry

Scientific paper

We derive simple forms for 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 theory and partially answer to some questions asked by J. Martinet and J.-P. Ramis in the 80's.

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