Geodesic
On the Łojasiewicz exponent of the gradient of a polynomial function
Annales Polonici Mathematici, Tome 71 (1999) no. 3, pp. 211-239.

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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.
DOI : 10.4064/ap-71-3-211-239
Keywords: polynomial mapping, Łojasiewicz exponent, Newton diagram

Andrzej Lenarcik 1

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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. http://geodesic.mathdoc.fr/articles/10.4064/ap-71-3-211-239/

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