On the Łojasiewicz exponent of the gradient of a polynomial function
Annales Polonici Mathematici, Tome 71 (1999) no. 3, pp. 211-239
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $h = ∑ h_{αβ} X^αY^β$ be a polynomial with complex coefficients. The Łojasiewicz exponent of the gradient of h at infinity is the least upper bound of the set of all real λ such that $|grad h(x,y)| ≥ c|(x,y)|^λ$ in a neighbourhood of infinity in ℂ², for c > 0. We estimate this quantity in terms of the Newton diagram of h. Equality is obtained in the nondegenerate case.
Keywords:
polynomial mapping, Łojasiewicz exponent, Newton diagram
Affiliations des auteurs :
Andrzej Lenarcik 1
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author = {Andrzej Lenarcik},
title = {On the {{\L}ojasiewicz} exponent of the gradient of a polynomial function},
journal = {Annales Polonici Mathematici},
pages = {211--239},
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volume = {71},
number = {3},
year = {1999},
doi = {10.4064/ap-71-3-211-239},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-71-3-211-239/}
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Andrzej Lenarcik. On the Łojasiewicz exponent of the gradient of a polynomial function. Annales Polonici Mathematici, Tome 71 (1999) no. 3, pp. 211-239. doi: 10.4064/ap-71-3-211-239
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