Typical one-parameter bifurcations of gradient flows with at most six singular points on the 2-sphere with holes
Dynamical Systems
2023-03-28 v1 Geometric Topology
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.
Keywords
Cite
@article{arxiv.2303.14975,
title = {Typical one-parameter bifurcations of gradient flows with at most six singular points on the 2-sphere with holes},
author = {Svitlana Bilun and Maria Loseva and Olena Myshnova and Alexandr Prishlyak},
journal= {arXiv preprint arXiv:2303.14975},
year = {2023}
}
Comments
17 pages, 19 figures. arXiv admin note: text overlap with arXiv:2303.10929