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

2023/03/27 by Svitlana Bilun, Bilun, Svitlana, Maria Loseva +5
Mathematics · Physics and Astronomy · #37c10 #37c15 #37c20 #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #G.1.7 #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2303.14975

openalex publication_date 2023/03/27 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28

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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