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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 278, Pages 29–33 (Mi tm3420)  
Interaction of the folded Whitney umbrella and swallowtail in slow–fast systems

I. A. Bogaevsky

Moscow State University, Moscow, Russia
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Abstract: The graph of a first integral of a smooth slow-fast system with two slow variables is a singular surface in the three-dimensional space; the variation of an external parameter on which the system depends gives rise to perestroikas ($=$transitions) of this surface. We find a normal form and present figures of the perestroika that describes the interaction between the swallowtail and folded Whitney umbrella on the graph of a first integral of a generic one-parameter family of such systems.
Received in May 2012
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 278, Pages 22–26
DOI: https://doi.org/10.1134/S008154381206003X
Bibliographic databases:
Document Type: Article
UDC: 515.164.15+517.928.4
Language: Russian
Citation: I. A. Bogaevsky, “Interaction of the folded Whitney umbrella and swallowtail in slow–fast systems”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 278, MAIK Nauka/Interperiodica, Moscow, 2012, 29–33; Proc. Steklov Inst. Math., 278 (2012), 22–26
Citation in format AMSBIB
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\paper Interaction of the folded Whitney umbrella and swallowtail in slow--fast systems
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
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\vol 278
\pages 29--33
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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