The Łojasiewicz Exponent at Infinity of Non-negative and Non-degenerate Polynomials

Abstract

Let f be a real polynomial, non-negative at infinity with non-compact zeroset. Suppose that f is non-degenerate in the Kushnirenko sense at infinity. In this paper we give a formula for the Łojasiewicz exponent at infinity of f and a formula for the exponent of growth of f in terms of its Newton polyhedron.