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The index of analytic vector fields and Newton polyhedra

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Bivià-Ausina C.

Fundamenta Mathematicae

2003

tom 177

nr 3

251-267

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.

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1 Fundamenta Mathematicae

1 Bivià-Ausina C.

1 2003

Wyniki wyszukiwania

The index of analytic vector fields and Newton polyhedra