arXiv subjects

Kateryna Semenovych

Publications and source records attributed to Kateryna Semenovych.

2 recordsLinked to original sources

arXiv2024

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

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.

math.DS↗

arXiv2024

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

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.

math.DS↗