Polynomial criteria for the \(v\)-sufficiency of jets in classes of finitely smooth mappings
type: Item
instance of: scholarly article
title: Polynomial criteria for the \(v\)-sufficiency of jets in classes of finitely smooth mappings
zbMATH Open document ID: 1213.58003
DOI: 10.1134/S106456241001028X
published in: Doklady Mathematics
publication date: 2010-11-17T00:00:00Z
review text: Let \(f: \mathbb R^n \rightarrow \mathbb R^m,\) \(n\geq m,\) be a \(C^{k}\)-smooth mapping, and let \(f^{r},\) \(r\leq k,\) be its \(r\)-truncation. The author studies conditions under which the solution sets of two systems of non-linear equations \(f(x)=0\) and \(f^{r}(x)=0\) are locally topologically equivalent. His idea is to formulate such conditions in terms of sufficiency problem for jets of mappings which was considered earlier in a similar context by Kuo, Kuiper, and others [\textit{T. C. Kuo}, Topology 8, 167--171 (1969; Zbl 0183.04601); Topology 11, 115--131 (1972; Zbl 0234.58005)].
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 58K15
zbMATH DE Number: 5816872
zbMATH Keywords: jets of mappings
zbMATH Keywords: sufficiency problem
zbMATH Keywords: nonlinear equations
author: Victor Kozyakin
reviewed by: Aleksandr G. Aleksandrov
MaRDI profile type: Publication
cites work: Stratifications and Finite Determinacy
cites work: On \(C^0\)-sufficiency of jets of potential functions
cites work: Sur le problème de la division
cites work: ASYMPTOTIC PROPERTIES OF POLYNOMIALS AND ALGEBRAIC FUNCTIONS OF SEVERAL VARIABLES
cites work: The Łojasiewicz exponent of an analytic function at an isolated zero
cites work: On the Łojasiewicz numbers
cites work: On the Łojasiewicz exponent and Newton polyhedron
cites work: Characterizations of v-sufficiency of jets
cites work: Singular Points of Complex Hypersurfaces. (AM-61)
full work available at URL: s106456241001028x
OpenAlex ID: W2076968298
description: scientific article; zbMATH DE number 5816872