Interaction of the folded Whitney umbrella and swallowtail in slow-fast systems
type: Item
instance of: scholarly article
title: Interaction of the folded Whitney umbrella and swallowtail in slow-fast systems
zbMATH Open document ID: 1323.34073
DOI: 10.1134/S008154381206003X
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2014-10-07T00:00:00Z
review text: The author considers a smooths slow-fast system defined by the equations \[ \varepsilon\dot s=S(s,x,y,\lambda),\quad \dot x= X(s,x,y,\lambda),\quad\dot y= Y(s,x,y,\lambda), \] where \(s\in\mathbb{R}\) is a fast variable, \(x,y\in\mathbb{R}\) are slow variables, \(\varepsilon,\lambda\in\mathbb{R}\) are constant parameters, \(\varepsilon\ll 1\). The graph of the first integral of this system is a singular surface in the three-dimensional space. ``The variation of the external parameter \(\lambda\) on which the system depends gives rise to transitions of this surface.'' The author has found a normal form and has presented ``figures of the transitions that describes the interaction between the swallowtail and folded Whitney umbrella on the graph of the first integral of a generic one-parameter family of such systems''.
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 6351767
zbMATH Keywords: smooth slow-fast system
zbMATH Keywords: vector fields
zbMATH Keywords: Legendrian submanifold
zbMATH Keywords: first integrals
zbMATH Keywords: Whitney umbrella
author: I. A. Bogaevskii
reviewed by: L. Socha
MaRDI profile type: Publication
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full work available at URL: s008154381206003x
OpenAlex ID: W2061585011
description: scientific article; zbMATH DE number 6351767