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

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...

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Bibliographic Details
Published in:arXiv.org 2023-03
Main Authors: Bilun, Svitlana, Loseva, Maria, Myshnova, Olena, Prishlyak, Alexandr
Format: Article
Language:English
Subjects:
Bifurcations
Gradient flow
Parameters
Saddles
Online Access:Get full text
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Summary: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.
ISSN:2331-8422