Briot-Bouquet’s Theorem in high dimension
ISSN: 0214-1493
Año de publicación: 2014
Número: 0
Páginas: 135-152
Tipo: Artículo
Otras publicaciones en: Publicacions matematiques
Resumen
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.