Some estimates of the Łojasiewicz gradient exponent at infinity near any fibre of a polynomial in two variables are given. An important point in the proofs is a new Charzyński-Kozłowski-Smale estimate of critical values of a polynomial in one variable.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-12,
author = {Janusz Gwo\'zdziewicz and Stanis\l aw Spodzieja},
title = {The \L ojasiewicz gradient inequality in a neighbourhood of the fibre},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {151-163},
zbl = {1108.14051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-12}
}
Janusz Gwoździewicz; Stanisław Spodzieja. The Łojasiewicz gradient inequality in a neighbourhood of the fibre. Annales Polonici Mathematici, Tome 85 (2005) pp. 151-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-12/