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This article is cited in 6 scientific papers (total in 6 papers)
Global bifurcations in generic one-parameter families with a separatrix loop on $S^2$
Yu. Ilyashenkoab, N. Solodovnikova a National Research University Higher School of Economics, 119048, Usacheva 6, Moscow, Russia
b Independent University of Moscow
Abstract:
Global bifurcations in the generic one-parameter families that unfold a vector field with a separatrix loop on the two-sphere are described. The sequence of bifurcations that occurs is in a sense in one-to-one correspondence with finite sets on a circle having some additional structure on them. Families under study appear to be structurally stable. The main tool is the Leontovich–Mayer–Fedorov (LMF) graph, analog of the separatrix sceleton and an invariant of the orbital topological classification of the vector fields on the two-sphere. Its properties and applications are described.
Key words and phrases:
bifurcation, separatrix loop, sparkling saddle connection.
Citation:
Yu. Ilyashenko, N. Solodovnikov, “Global bifurcations in generic one-parameter families with a separatrix loop on $S^2$”, Mosc. Math. J., 18:1 (2018), 93–115
Linking options:
https://www.mathnet.ru/eng/mmj664 https://www.mathnet.ru/eng/mmj/v18/i1/p93
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Abstract page: | 276 | References: | 50 |
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