Bifurcations of ordinary differential equations of Clairaut type
type: Item
instance of: scholarly article
title: Bifurcations of ordinary differential equations of Clairaut type
zbMATH Open document ID: 1021.37031
DOI: 10.1016/S0022-0396(02)00198-5
author: Masatomo Takahashi
published in: Journal of Differential Equations
publication date: 2003-06-17T00:00:00Z
review text: The paper deals with a one-parameter family of Clairaut type equations. In order to pursue the classification the author uses Legendrian singularity theory and the notion of Legendrian unfoldings. Normal forms are represented by one-parameter integral diagrams, which are divergent diagrams of map germs.
reviewed by: Abdelkader Boucherif
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 58K50
Mathematics Subject Classification ID: 34C40
Mathematics Subject Classification ID: 34A26
zbMATH DE Number: 1929524
zbMATH Keywords: bifurcation
zbMATH Keywords: ordinary differential equations of Clairaut type
zbMATH Keywords: singularity theory
zbMATH Keywords: normal forms
MaRDI profile type: Publication
cites work: Isotopies of generic plane curves
cites work: The unfolding and determinacy theorems for subgroups of 𝒜 and 𝒦
cites work: Q3862121
cites work: CLASSIFICATION OF GENERIC INTEGRAL DIAGRAMS AND FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
cites work: The theory of Legendrian unfoldings and first-order differential equations
cites work: Completely integrable holonomic systems of first-order differential equations
cites work: Holonomic systems of Clairaut type
cites work: LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
cites work: Reconstructions of fronts and caustics depending on a parameter and versality of mappings
full work available at URL: s0022-0396(02)00198-5
OpenAlex ID: W2054583842
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description: scientific article; zbMATH DE number 1929524