Structure of optimal gradient flows bifurcations on closed surfaces
Autor: | Ovtsynov, Illia, Prishlyak, Alexandr |
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Rok vydání: | 2024 |
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Druh dokumentu: | Working Paper |
Popis: | We consider structure of typical gradient flows bifurcations on closed surfaces with minimal number of singular points. There are two type of such bifurcations: saddle-node (SN) and saddle connections (SC). The structure of a bifurcation is determinated by codimension one flow in the moment of bifurcation. We use the chord diagrams to specify the flows up to topological trajectory equivivalence. A chord diagram with a marked arc is complete topological invariant of a SN-bifurcations and a chord diagram with T-insert -- of SC-bifurcations. We list all such diagrams for flows on norientable surfaces of genus at most 2 and nonorientable surfaces of genus at most 3. For each of diagram we found inverse one that correspond the inverse flow. Comment: 15 pages, 11 figures |
Databáze: | arXiv |
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