Global Bifurcations in Generic One-parameter Families on \(\mathbb{S}^2\)

Resumo

In this paper we prove that generic one-parameter families of vector fields on \(\mathbb{S}^2\) in the neighborhood of the fields of classes AH, SN, HC, SC (Andronov–Hopf, saddle-node, homoclinic curve, saddle connection) are structurally stable. We provide a classification of bifurcations in these families.