Felipe Cano

Hypersurfaces intégrales des feuilletages holomorphes

© Annales de l’institut Fourier, 1992, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Dicritical logarithmic foliations

We show Che existence of weak logarithmic modeis for any (dicritical or not) holomorphir foliation Y of (C5, 0) without saddlenodes lo its desingularization. The modeis are written in lerma of a representative set of separatrices, whose equisingularity types are rontrolled by the Milnor number of the foliation.

Secants of Trajectories in Dimension Three

In this paper we give a description of the sets of accumulation of secants for orbits of real analytic vector fields in dimension three with the origin as only ω-limit point. It is an infinitesimal version of the Poincare-Bendixson problem in dimension three. These sets have structure of cyclic graph when the singularities are isolated under one blow-up. If the reduction of singularities is hyperbolic, under conditions of Morse-Smale type, we prove that the accumulation set is a single point or homeomorphic to \({\mathbb{S}}^{1}\).

Blowings-Up of Vector Fields

A new proof of the reduction of singularities for planar vector fields is presented. The idea is to adapt Zariski’s local uniformisation method to the vector field setting.