Bifurcations and Structural Stability of Generic PC-HC Families

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.