The structure of Morse flows and co-dimension one gradient flows on the sphere with holes
Dynamical Systems
2026-01-13 v1
Abstract
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.
Cite
@article{arxiv.2601.06926,
title = {The structure of Morse flows and co-dimension one gradient flows on the sphere with holes},
author = {Illia Ovtsynov and Alexandr Prishlyak},
journal= {arXiv preprint arXiv:2601.06926},
year = {2026}
}
Comments
19 pages, 12 figures