Briot-Bouquet's Theorem in high dimension
Carrillo Torres, Sergio Alejandro (Universidad de Valladolid. Departamento de Algebra, Análisis Matemático, Geometría y Topología)
Sanz Sánchez, Fernando (Universidad de Valladolid. Departamento de Algebra, Análisis Matemático, Geometría y Topología)

Date:	2014
Abstract:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Holomorphic vector elds ; Formal and convergent invariant manifolds ; Non-resonance ; Briot-Bouquet's Theorem ; Stable analytic manifold
Published in:	Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 135-152, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287205
DOI: 10.5565/PUBLMAT_Extra14_07

18 p, 359.4 KB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles