On the Lojasiewicz exponents of quasi-homogeneous functions

Alain Haraux (1) , Tien Son Pham (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 DEPARTMENT OF MATHEMATICS - Department of Mathematics

Quasi-homogeneous functions, and especially polynomials, enjoy some specific properties around the origin which allow to estimate the so-called Lojasiewicz exponents in a way quite similar to homogeneous functions. In particular we generalize a previous result for polynomials of two variables concerning the optimal Lojasiewicz gradient inequality at the origin.

Mots clés: quasi-homogeneous; gradient inequality; Lojasiewicz exponents

Domaines: Analyse numérique [math.NA]

Alain Haraux, Tien Son Pham. On the Lojasiewicz exponents of quasi-homogeneous functions. 2007. ⟨hal-00177816⟩