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Regular version of the site

Article

Global bifurcations in generic one-parameter families with a separatrix loop on S^2

Moscow Mathematical Journal. 2018. Vol. 18. No. 1. P. 93-115.
Ilyashenko Y., Solodovnikov N.

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 bifurcation that occurs is in a sense in ono-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 - an invariant of the orbital topological classification of the vector fields on the two-sphere. Its properties and applications are described.