On The Effective Computation Of Łojasiewicz Exponents Via Newton Polyhedra

Abstract

In this paper we give some conclusions on Newton non-degenerate analytic map germs on Kn (K = ℝ or ℂ), using information from their Newton polyhedra. As a consequence, we obtain the exact value of the Lojasiewicz exponent at the origin of Newton non-degenerate analytic map germs. In particular, we establish a connection between Newton non-degenerate ideals and their integral closures, thus leading to a simple proof of a result of Saia. Similar results are also considered to polynomial maps which are Newton non-degenerate at infinity.