The index of analytic vector fields and Newton polyhedra

• Autorzy: Carles Bivià-Ausina
• Języki publikacji: EN

Abstrakty

EN

We prove that if f:(ℝⁿ,0) → (ℝⁿ,0) is an analytic map germ such that $f^{-1}(0) = {0}$ and f satisfies a certain non-degeneracy condition with respect to a Newton polyhedron Γ₊ ⊆ ℝⁿ, then the index of f only depends on the principal parts of f with respect to the compact faces of Γ₊. In particular, we obtain a known result on the index of semi-weighted-homogeneous map germs. We also discuss non-degenerate vector fields in the sense of Khovanskiĭand special applications of our results to planar analytic vector fields.

Kategorie tematyczne

• 32S05: Local singularities
• 57R45: Singularities of differentiable mappings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 177
• Numer: 3
• Strony: 251-267

Daty

wydano

2003

Twórcy

autor

Carles Bivià-Ausina

• Departament de Matemàtica Aplicada, Universitat Politècnica de València, Escola Politècnica Superior d'Alcoi, Plaça Ferrándiz i Carbonell 2, 03801 Alcoi (Alacant), Spain

Identyfikatory

DOI

10.4064/fm177-3-5