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
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Record created 2014-05-19, last modified 2022-09-04