Versal deformation of the analytic saddle-node
Loray, Frank
HAL, hal-00001192 / Harvested from HAL
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.
Publié le : 2004-07-05
Classification:  normal forms,  saddle-nodes,  singularities,  Foliations,  32S65,  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]
@article{hal-00001192,
     author = {Loray, Frank},
     title = {Versal deformation of the analytic saddle-node},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00001192}
}
Loray, Frank. Versal deformation of the analytic saddle-node. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00001192/