Đề tài " A preparation theorem for codimension-one foliations "

Dedicated to C´sar Camacho for his 60th birthday e Abstract After gluing foliated complex manifolds, we derive a preparation-like theorem for singularities of codimension-one foliations and planar vector fields (in the real or complex setting). Without computation, we retrieve and improve results of Levinson-Moser for functions, Dufour-Zhitomirskii for nondegenerate ˙ codimension-one foliations (proving in turn the analyticity), Str´zyna-Zoladek o˙ ´ for non degenerate planar vector fields and Bruno-Ecalle for saddle-node foliations in the plane. .

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