Per citar aquest document: http://ddd.uab.cat/record/118298
Briot-Bouquet’s Theorem in high dimension
Carrillo, S. A. (Universidad de Valladolid. Departamento de Algebra, Análisis Matemático, Geometría y Topología)
Sanz, F. (Universidad de Valladolid. Departamento de Algebra, Análisis Matemático, Geometría y Topología)

Data: 2014
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Holomorphic vector elds ; Formal and convergent invariant manifolds ; Non-resonance ; Briot-Bouquet's Theorem ; Stable analytic manifold
Publicat a: Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 135-152, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_Extra14_07


18 p, 359.4 KB

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