The real part of the decomposition of a polynomial and its determinacy
type: Item
instance of: scholarly article
title: The real part of the decomposition of a polynomial and its determinacy
zbMATH Open document ID: 0893.58011
DOI: 10.1007/BF02362650
author: Guo-Bin Zhang
author: Weizhi Sun
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-07-26T00:00:00Z
review text: It is known that the set of topological equivalence classes of real polynomials in \(n\) variables of degree not exceeding \(k\) is a finite set [\textit{T. Fukuda}, Inst. Haut. Étud. Sci., Publ. Math. 46, 87-106 (1976; Zbl 0341.57019)]. The authors prove that for \(n \geq 2\) the set of those classes for all \(k\) is infinite. This statement is an immediate consequence of a simple criterion that describes when homogeneous polynomial-germs defined on \(({\mathbb{R}}^2, 0)\) are \(C^0\)-finitely determined.
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 32S15
Mathematics Subject Classification ID: 32S25
zbMATH DE Number: 1017616
zbMATH Keywords: \(C^0\)-determinacy
zbMATH Keywords: \(r\)-jets equivalence
zbMATH Keywords: topological equivalence
zbMATH Keywords: Puiseux series
zbMATH Keywords: real polynomials
zbMATH Keywords: homogeneous polynomials
reviewed by: Aleksandr G. Aleksandrov
MaRDI profile type: Publication
cites work: Types topologiques des polynômes
cites work: Sufficiency of jets in \(J^ r(2,1)\) via decomposition
cites work: On \(C^0\)-sufficiency of jets of potential functions
cites work: Q4769677
cites work: Singularity theory and an introduction to catastrophe theory
full work available at URL: https://doi.org/10.1007/bf02362650
OpenAlex ID: W2028023861
description: scientific article; zbMATH DE number 1017616