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arXiv:2303.14975 [math.DS]AbstractReferencesReviewsResources

Typical one-parameter bifurcations of gradient flows with at most six singular points on the 2-sphere with holes

Svitlana Bilun, Maria Loseva, Olena Myshnova, Alexandr Prishlyak

Published 2023-03-27Version 1

We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of flows is at most six. To describe structures, we separatrix diagrams of flows. The saddle-node singularity is specified by selecting a separatrix in the diagram of the flow befor the bifurcation and the saddle connection is specified by a separatrix, which conect two saddles.

Comments: 17 pages, 19 figures. arXiv admin note: text overlap with arXiv:2303.10929
Categories: math.DS, math.GT
Subjects: G.1.7
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