English

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