\(C^l-{\mathcal G}_v\)-determinacy of weighted homogeneous function germs on weighted homogeneous analytic varieties
type: Item
instance of: scholarly article
title: \(C^l-{\mathcal G}_v\)-determinacy of weighted homogeneous function germs on weighted homogeneous analytic varieties
zbMATH Open document ID: 1154.58021
author: Dun-mu Zhang
author: Hengxing Liu
published in: Hokkaido Mathematical Journal
publication date: 2008-07-29T00:00:00Z
review text: The authors provide estimates on the degree of \( C^l-{\mathcal G}_V \)-determinacy (where \( \mathcal G \) is one of Mather's groups \( \mathcal R \) or \( \mathcal K \)) of weighted homogeneous function germs defined on a weighted homogeneous analytic variety \( V \) and satisfying a suitable Łojasiewicz condition. They give an explicit order such that the \( C^l \) geometric structure of a weighted homogeneous polynomial is preserved under higher order perturbations. This extends results on \( C^l-{\mathcal K} \) determinacy of homogeneous functions germs given by \textit{M. A. Soares Ruas} [Math. Scand. 59, No.~1, 59--70 (1986; Zbl 0632.58013)] and \textit{M. A. Soares Ruas} and \textit{M. J. Saia} [Hokkaido Math. J. 26, No.~1, 89--99 (1997; Zbl 0873.58010)].
reviewed by: Vincent Thilliez
Mathematics Subject Classification ID: 58K40
Mathematics Subject Classification ID: 58A35
Mathematics Subject Classification ID: 32C05
zbMATH DE Number: 5305077
zbMATH Keywords: finite determinacy
zbMATH Keywords: weighted homogeneous polynomials
zbMATH Keywords: weighted homogeneous analytic varieties
zbMATH Keywords: controlled vector fields
zbMATH Keywords: Lojasiewicz inequalities
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1253539557
OpenAlex ID: W2049845757
DOI: 10.14492/HOKMJ/1253539557
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description: scientific article; zbMATH DE number 5305077