Bifurcations and Structural Stability of Generic PC-HC Families

TL;DR

This paper investigates the structural stability and bifurcation behavior of generic vector field families on the 2-sphere, providing classification, invariants, and bifurcation diagrams.

Contribution

It establishes the structural stability of generic PC-HC vector field families and classifies them using invariants near bifurcation supports.

Findings

Proves the structural stability of generic PC-HC families on S^2.

Provides a classification scheme based on configuration and characteristic set.

Constructs bifurcation diagrams for these families.

Abstract

In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere $S^2$ 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.