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Un théorème de fonctions implicites. Applications

Francis Sergeraert (1973)

Annales de l'institut Fourier

On énonce un théorème de fonctions implicites du type de Nash-Moser, et on indique une application à l’étude des singularités de fonctions différentiables réelles (problème du déploiement universel de Thom).

Unfoldings of foliations with multiform first integrals

Tatsuo Suwa (1983)

Annales de l'institut Fourier

Let F = ( ω ) be a codim 1 local foliation generated by a germ ω of the form ω = f 1 ... f p i = 1 p λ i d f i f i for some complex numbers λ i and germs f i of holomorphic functions at the origin in C n . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of F . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for F is equivalent to the unfolding theory for the multiform function...

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