Global {\L}ojasiewicz inequalities on comparing the rate of growth of polynomial functions

TL;DR

This paper establishes a global version of the {\

Contribution

It introduces a global {\

Findings

Non-degeneracy at infinity is generic among polynomial functions.

Provides a global {\

,

Abstract

We present a global version of the {\L}ojasiewicz inequality on comparing the rate of growth of two polynomial functions in the case the mapping defined by these functions is (Newton) non-degenerate at infinity. In addition, we show that the condition of non-degeneracy at infinity is generic in the sense that it holds in an open and dense semi-algebraic set of the entire space of input data.