The structure of Morse flows and co-dimension one gradient flows on the sphere with holes

Illia Ovtsynov; Alexandr Prishlyak

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arXiv · 2601.06926

The structure of Morse flows and co-dimension one gradient flows on the sphere with holes

Illia Ovtsynov·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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Illia Ovtsynov, Alexandr Prishlyak. 2026-01-11. The structure of Morse flows and co-dimension one gradient flows on the sphere with holes. https://arxiv.org/abs/2601.06926

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