Briot-Bouquet’s Theorem in high dimension

  1. Carrillo, S. A.
  2. Sanz, F.
Revue:
Publicacions matematiques

ISSN: 0214-1493

Année de publication: 2014

Número: 0

Pages: 135-152

Type: Article

DOI: 10.5565/PUBLMAT_EXTRA14_07 DIALNET GOOGLE SCHOLAR lock_openDDD editor

D'autres publications dans: Publicacions matematiques

Résumé

Let X be a germ of holomorphic vector field at 0 2 Cn and let E be a linear subspace of Cn which is invariant for the linear part of X at 0. We give a suficient condition that imply the existence of a non-singular invariant manifold tangent to E at 0. It generalizes to higher dimensions the conditions in the classical Briot{Bouquet's Theorem: roughly speaking, we impose that the convex hull of the eigenvalues ui corresponding to E does not contain 0 and there are no resonances between the ui and the complementary eigenvalues. As an application, we propose an elementary proof of the analyticity of the local stable and unstable manifolds of a real analytic vector field at a singular point.