Currently displaying 1 – 15 of 15

Showing per page

Order by Relevance | Title | Year of publication

Instability of equilibria in dimension three

Marco Brunella — 1998

Annales de l'institut Fourier

In this paper we show that if v is an analytic vector field on 3 having an isolated singular point at 0, then there exists a trajectory of v which converges to 0 in the past or in the future. The proof is based on certain results concerning desingularizaton of vector fields in dimension three and on index-type arguments .

Foliations on the complex projective plane with many parabolic leaves

Marco Brunella — 1994

Annales de l'institut Fourier

We prove that a foliation on C P 2 with hyperbolic singularities and with “many" parabolic leaves (i.e. leaves without Green functions) is in fact a linear foliation. This is done in two steps: first we prove that there exists an algebraic leaf, using the technique of harmonic measures, then we show that the holonomy of this leaf is linearizable, from which the result follows easily.

Some remarks on indices of holomorphic vector fields.

Marco Brunella — 1997

Publicacions Matemàtiques

One can associate several residue-type indices to a singular point of a two-dimensional holomorphic vector field. Some of these indices depend also on the choice of a separatrix at the singular point. We establish some relations between them, especially when the singular point is a generalized curve and the separatrix is the maximal one. These local results have global consequences, for example concerning the construction of logarithmic forms defining a given holomorphic foliation.

Page 1

Download Results (CSV)