Bifurcation diagrams and caustics of simple quasi border singularities
type: Item
instance of: scholarly article
title: Bifurcation diagrams and caustics of simple quasi border singularities
zbMATH Open document ID: 1250.58014
author: Fawaz Alharbi
published in: Topology and its Applications
publication date: 2012-03-02T00:00:00Z
review text: This paper is devoted to the study of two types of equivalence relations in the space of germs of functions, namely quasi boundary and quasi corner equivalences which were defined in [\textit{V. M. Zakalyukin}, Banach Center Publications 82, 215--225 (2008; Zbl 1151.58024)] and [\textit{F. D. Alharbi} and \textit{V. M. Zakalyukin}, Proc. Steklov Inst. Math. 270, 1--14 (2010) and Trudy Mat. Inst. Steklova 270, 7--20 (2010; Zbl 1225.58017)]. These equivalences are a slight modification of pseudo boundary and pseudo corner equivalences and behave well when the function germs depend on parameters. They play an intermediate role between right equivalence (diffeomorphisms action in the source space) and boundary equivalence (right equivalence preserving a smooth hypersurface). In Section 2 the author gives the main definitions and states the simple singularities and their versal deformations with respect to both equivalence relations. Section 3 explains the correspondence to the classification of Lagrangian projections with a boundary or a corner. Section 4 describes the bifurcation diagrams and the caustics for the simple quasi boundary (corner) singularities. Finally, Section 5 gives an algebraic description of the equivalence classes.
Mathematics Subject Classification ID: 58K05
Mathematics Subject Classification ID: 58K40
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 6011288
zbMATH Keywords: quasi border singularities
zbMATH Keywords: bifurcation diagram
zbMATH Keywords: caustic
zbMATH Keywords: Lagrangian projection
reviewed by: Raúl Oset Sinha
MaRDI profile type: Publication
full work available at URL: j.topol.2011.09.011
OpenAlex ID: W1966226214
cites work: Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol'd
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cites work: Quasi-projections
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cites work: Genericity of caustics and wavefronts on an \(r\)-corner
DOI: 10.1016/J.TOPOL.2011.09.011
description: scientific article; zbMATH DE number 6011288