A preparation theorem for codimension-one foliations

Autores: Frank Loray
Localización: Annals of mathematics, ISSN 0003-486X, Vol. 163, Nº 2, 2006, págs. 709-722
Idioma: inglés
DOI: 10.4007/annals.2006.163.709
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Resumen
- 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.