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/