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

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.