The structure of Morse flows and co-dimension one gradient flows on the sphere with holes
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| Format: | Preprint |
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2026
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| _version_ | 1866912817260527616 |
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| author | Ovtsynov, Illia Prishlyak, Alexandr |
| author_facet | Ovtsynov, Illia Prishlyak, Alexandr |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06926 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The structure of Morse flows and co-dimension one gradient flows on the sphere with holes Ovtsynov, Illia Prishlyak, Alexandr Dynamical Systems 37c10, 37c15, 37c20 G.1.7 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. |
| title | The structure of Morse flows and co-dimension one gradient flows on the sphere with holes |
| topic | Dynamical Systems 37c10, 37c15, 37c20 G.1.7 |
| url | https://arxiv.org/abs/2601.06926 |