A preparation theorem for codimension one foliations
Abstract
After gluing foliated complex manifolds,we derive a preparation-like theorem for singularitiesof codimension one foliations and planar vector fields(in the real or complex setting). Without computation, we retrieve and improve resultsof Levinson-Moser for functions, Dufour-Zhitomirskii for non degenerate codimension 1 foliations(proving in turn the analyticity),Strozyna-Zoladek for non degenerate planar vector fieldsand Brjuno-Ecalle for saddle-node foliations in the plane.
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