The index of analytic vector fields and Newton polyhedra

@article{CarlesBivià2003,
abstract = {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.},
author = {Carles Bivià-Ausina},
journal = {Fundamenta Mathematicae},
keywords = {index of a vector field; real-analytic functions; Newton polyhedra},
language = {eng},
number = {3},
pages = {251-267},
title = {The index of analytic vector fields and Newton polyhedra},
url = {http://eudml.org/doc/282640},
volume = {177},
year = {2003},
}

TY - JOUR
AU - Carles Bivià-Ausina
TI - The index of analytic vector fields and Newton polyhedra
JO - Fundamenta Mathematicae
PY - 2003
VL - 177
IS - 3
SP - 251
EP - 267
AB - 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.
LA - eng
KW - index of a vector field; real-analytic functions; Newton polyhedra
UR - http://eudml.org/doc/282640
ER -