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arXiv · 2303.14975

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
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Abstract

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.

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Svitlana Bilun, Maria Loseva, Olena Myshnova, Alexandr Prishlyak. 2023-03-27. Typical one-parameter bifurcations of gradient flows with at most six singular points on the 2-sphere with holes. https://arxiv.org/abs/2303.14975

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