The Łojasiewicz numbers and plane curve singularities

Evelia García Barroso; Tadeusz Krasiński; Arkadiusz Płoski

Evelia García Barroso ; Tadeusz Krasiński ; Arkadiusz Płoski

Annales Polonici Mathematici, Tome 85 (2005), p. 127-150 / Harvested from The Polish Digital Mathematics Library

Résumé

For every holomorphic function in two complex variables with an isolated critical point at the origin we consider the Łojasiewicz exponent ₀(f) defined to be the smallest θ > 0 such that ${| g r a d f (z) | \geq c | z |}^{θ}$ near 0 ∈ ℂ² for some c > 0. We investigate the set of all numbers ₀(f) where f runs over all holomorphic functions with an isolated critical point at 0 ∈ ℂ².

Publié le : 2005-01-01

Zbl 1095.32010

EUDML-ID : urn:eudml:doc:280347

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-11,
     author = {Evelia Garc\'\i a Barroso and Tadeusz Krasi\'nski and Arkadiusz P\l oski},
     title = {The \L ojasiewicz numbers and plane curve singularities},
     journal = {Annales Polonici Mathematici},
     volume = {85},
     year = {2005},
     pages = {127-150},
     zbl = {1095.32010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-11}
}

Evelia García Barroso; Tadeusz Krasiński; Arkadiusz Płoski. The Łojasiewicz numbers and plane curve singularities. Annales Polonici Mathematici, Tome 85 (2005) pp. 127-150. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-11/