Structure of Morse flows with at most six singular points on the torus with a hole

2024/04/02 by Maria Loseva, Loseva, Maria, Alexandr Prishlyak +5
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2404.02223

Abstract

We describe all possible topological structures of Morse flows and typical gradient saddle-nod bifurcation of flows on the 2-dimensional torus with a hole in the case that the number of singular point of flows is at most six. To describe structures, we use separatrix diagrams of flows. The saddle-node bifurcation is specified by selecting a separatrix in the separatrix diagram of the flow befor the bifurcation.

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