Geodesic
Interaction of the folded Whitney umbrella and swallowtail in slow--fast systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 29-33

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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. 
@article{TM_2012_278_a2,
     author = {I. A. Bogaevsky},
     title = {Interaction of the folded {Whitney} umbrella and swallowtail in slow--fast systems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {29--33},
     publisher = {mathdoc},
     volume = {278},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_278_a2/}
}
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I. A. Bogaevsky. Interaction of the folded Whitney umbrella and swallowtail in slow--fast systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 29-33. http://geodesic.mathdoc.fr/item/TM_2012_278_a2/