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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 3, Pages 88–94
DOI: https://doi.org/10.4213/faa163 (Mi faa163) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

On the Stability of Bifurcation Diagrams of Vanishing Flattening Points

R. Uribe-Vargas

Université Paris VII – Denis Diderot
Full-text PDF (167 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa163
Abstract: On a smooth surface in Euclidean $3$-space, we consider vanishing curves whose projections on a given plane are small circles centered at the origin. The bifurcations diagram of a parameter-dependent surface is the set of parameters and radii of the circles corresponding to curves with degenerate flattening points.
Solving a problem due to Arnold, we find a normal form of the first nontrivial example of a flattening bifurcation diagram, which contains one continuous invariant.
Keywords: flattening point, bifurcation diagram, singularity of a family of mappings.
Received: 13.05.2002
English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 3, Pages 236–240
DOI: https://doi.org/10.1023/A:1026096919765
Bibliographic databases:
Document Type: Article
UDC: 514.75
Language: Russian
Citation: R. Uribe-Vargas, “On the Stability of Bifurcation Diagrams of Vanishing Flattening Points”, Funktsional. Anal. i Prilozhen., 37:3 (2003), 88–94; Funct. Anal. Appl., 37:3 (2003), 236–240
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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