Bifurcations and Structural Stability of Generic PC-HC Families
Dynamical Systems
2026-05-14 v1
Abstract
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. Furthermore, bifurcation diagrams for the considered class of families are constructed.
Cite
@article{arxiv.2605.12636,
title = {Bifurcations and Structural Stability of Generic PC-HC Families},
author = {Alexey Dorovskiy},
journal= {arXiv preprint arXiv:2605.12636},
year = {2026}
}
Comments
35 pages, 12 figures. Accepted for publication in Transactions of the Moscow Mathematical Society (Trudy Moskovskogo Matematicheskogo Obshchestva)