On the Łojasiewicz exponent of the gradient of a polynomial function
Andrzej Lenarcik
Annales Polonici Mathematici, Tome 72 (1999), p. 211-239 / Harvested from The Polish Digital Mathematics Library
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Let h=∑hαβXαYβ 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 |gradh(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.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:262851 
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Andrzej Lenarcik. On the Łojasiewicz exponent of the gradient of a polynomial function. Annales Polonici Mathematici, Tome 72 (1999) pp. 211-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv71z3p211bwm/

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