Heteroclinic bifurcations of \(\Omega\)-stable vector fields on \(3\)-manifolds (Q1576779)

This paper deals with stability of families of vector fields, that are defined on 3D manifolds and whose nonwandering sets are structurally stable. To this end the author introduces a notion of stability which is suitable for studying the geometry and dynamics on stable and unstable sets. Then, for a class of one parameter families consisting of \(\Omega\)-stable vector fields on a 3-D compact manifold, the author classifies the stable ones with respect to this notion of stability.