Global {\L}ojasiewicz inequalities on comparing the rate of growth of polynomial functions
Sĩ Tiệp Đinh, Feng Juan Guo, Tiến-Sơn Phạm · arXiv (Cornell University) · 2019
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.