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Bifurcation values of families of real curves

Part of: Families, fibrations Singularities Theory of singularities and catastrophe theory Differential topology

Published online by Cambridge University Press:  31 May 2017

Cezar Joiţa  and
Mihai Tibăr
Cezar Joiţa
Affiliation:
Institute of Mathematics of the Romanian Academy, Laboratoire Européen Associé CNRS Franco-Roumain Math-Mode, PO Box 1-764, 014700 Bucureşti, Romania (cezar.joita@imar.ro)
Mihai Tibăr
Affiliation:
Université de Lille, CNRS, UMR 8524, Laboratoire Paul Painlevé, 59000 Lille, France (tibar@math.univ-lille1.fr)
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The detection of the bifurcation set of polynomial mapping ℝn → ℝp, n ⩾ p, in more than two variables remains an unsolved problem. In this note we provide a solution for n = p + 1 ⩾ 3.

Keywords

bifurcation locuspolynomials mapfibration

MSC classification

Secondary: 14D06: Fibrations, degenerations 58K05: Critical points of functions and mappings 57R45: Singularities of differentiable mappings 14P10: Semialgebraic sets and related spaces 32S20: Global theory of singularities; cohomological properties 58K15: Topological properties of mappings
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 6 , December 2017 , pp. 1233 - 1242
Copyright
Copyright © Royal Society of Edinburgh 2017