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Global Łojasiewicz inequalities on comparing the rate of growth of polynomial functions

We present a global version of the Łojasiewicz 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.

preprint2021arXivOpen access
Si-Tiep DinhFeng GuoTien-Son Pham
math.AG
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Open access3 authors1 topic
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Si-Tiep DinhFeng GuoTien-Son Pham

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