Olena Myshnova | Searcharxiv

arXiv2023

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

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.

math.DS↗

arXiv2023

Structures of optimal discrete gradient vector fields on surface with one or two critical cells

We describe all possible structures of discrete vector field (discrete Morse functions) with minimal number of critical cells on the regular CW-complex for the 2-disk (1 cell), the 2-sphere (2 cells), the cylinder (2 cells) and Mobius band (2 cells).

math.DS↗