On the Łojasiewicz exponents of quasi-homogeneous functions

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

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Abstract:

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.

Keywords:

quasi-homogeneous, gradient inequality, Łojasiewicz exponents

Mathematical Subject Classification:

14P10, 14P15, 32S05, 34A26

Author(s) information: