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Resumen de A preparation theorem for codimension-one foliations

Frank Loray Árbol académico

  • 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¿oÿzyna- ÿ Zoladek for non degenerate planar vector fields and Bruno-¿Ecalle for saddle-node foliations in the plane.


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