# The index of analytic vector fields and Newton polyhedra

Bivia-Ausina, CARLES The index of analytic vector fields and Newton polyhedra. In: Mathematical Society of Japan, 12th International Research Insitute, Singularity Theory and Its Applications, 16-25 September 2003, Sapporo Convention Center ( Sapporo, Japan ).

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17 September 2003: Mathematical Society of Japan, 12th International Research Insitute, Singularity Theory and Its Applications

## Abstract

In this work we study a condition of non-degeneracy on analytic maps (R_n; 0) \to (R_n; 0) using the language of Newton polyhedra. When f:(R_n; 0) \to (R_n; 0) satisfies this condition and f^{-1}(0) = {0} , we obtain a result on the invariance of the local index of f under the summation of suitable monomials to each component function of f.

Item Type: Conference or Workshop Item (UNSPECIFIED) 53-xx DIFFERENTIAL GEOMETRY 61