On the Łojasiewicz exponents of quasi-homogeneous functions

Alain Haraux and Tien Son Phạm

Journal of Singularities
volume 11 (2015), 52-66

Received: 29 June 2013. Received in revised form: 16 April 2015.

DOI: 10.5427/jsing.2015.11c

Add a reference to this article to your citeulike library.


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


quasi-homogeneous, gradient inequality, Łojasiewicz exponents

Mathematical Subject Classification:

14P10, 14P15, 32S05, 34A26

Author(s) information:

Alain Haraux Tien Son Phạm
Laboratoire Jacques-Louis Lions Department of Mathematics
U.M.R C.N.R.S. 7598 Dalat University
Université Pierre et Marie Curie Dalat, Vietnam
Boîte courrier 187, 75252 Paris Cedex 05, France
75252 Paris Cedex 05, France
email: haraux@ann.jussieu.fr email: sonpt@dlu.edu.vn