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Abstract

We prove that if $f:(\mathbb R^n,0)\to (\mathbb R^n,0)$ 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 ${\mit\Gamma}_+\subseteq\mathbb R^n$, then the index of $f$ only depends on the principal parts of $f$ with respect to the compact faces of ${\mit\Gamma}_+$. 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 Khovanski\u\i and special applications of our results to planar analytic vector fields.