A preparation theorem for codimension one foliations

Details A preparation theorem for codimension one foliations A preparation theorem for codimension one foliations

2004-02-25

arxiv.org/abs/math/0402411v1

Annals of Mathematics 163, 2 (2006) 709--722

Mathematics

Differential Geometry

Scientific paper

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 non degenerate codimension 1 foliations (proving in turn the analyticity), Strozyna-Zoladek for non degenerate planar vector fields and Brjuno-Ecalle for saddle-node foliations in the plane.

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