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Journal Articles Annals of Mathematics Year : 2006

A preparation theorem for codimension one foliations

Frank Loray

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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hal-00001190 , version 1 (25-02-2004)

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Frank Loray. A preparation theorem for codimension one foliations. Annals of Mathematics, 2006, 163 (2), pp.709--722. ⟨hal-00001190⟩
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