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), Stró\.zyna-\.Zo\l adek for non degenerate planar vector fields and Bruno-Écalle for saddle-node foliations in the plane.
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