Structure of the codimesion one gradient flows with at most six singular points on the Möbius strip

2024/04/04 by Maria Loseva, Alexandr Prishlyak, Loseva, Maria +5
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2404.07233

Abstract

We describe all possible topological structures of Morse flows and typical one-parametric gradient bifurcation on the Möbius strip in the case that the number of singular point of flows is at most six. To describe structures, we use the separatrix diagrams of flows. The saddle-node bifurcation is specified by selecting a separatrix in the diagram of the Morse flow befor the bifurcation and the saddle connection is specified by a separatrix, which connect two saddles on the diagram.

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