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Tr. Mat. Inst. 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

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 278, 22–26

Bibliographic databases:

UDC: 515.164.15+517.928.4
Received in May 2012

Citation: I. A. Bogaevsky, “Interaction of the folded Whitney umbrella and swallowtail in slow–fast systems”, Differential equations and dynamical systems, Collected papers, Tr. 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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\by I.~A.~Bogaevsky
\paper Interaction of the folded Whitney umbrella and swallowtail in slow--fast systems
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2012
\vol 278
\pages 29--33
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 278
\pages 22--26
\crossref{https://doi.org/10.1134/S008154381206003X}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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