On the Lojasiewicz exponents of quasi-homogeneous functions

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2015 France Publisher:Journal of SingularitiesJournal:Journal of Singularities (eissn: 1949-2006,

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Authors: Haraux, Alain; Pham, Tien Son;

doi: 10.5427/jsing.2015.11c

On the Lojasiewicz exponents of quasi-homogeneous functions

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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 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.

Country

France

Related Organizations

French National Centre for Scientific Research
France
Sorbonne Université
France
Sorbonne University
France
Laboratoire Jacques-Louis Lions
France
Dalat University
Viet Nam

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Keywords

Real-analytic and semi-analytic sets, quasi-homogeneous mapping, Local complex singularities, quasi-homogeneous function, [MATH] Mathematics [math], Semialgebraic sets and related spaces, Łojasiewicz exponent, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA]

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