Structural stability of vector fields on 3-manifolds with boundary

AbstractFrom the structural stability viewpoint vector fields on M which are tangent to the boundary of M are analysed. A class of vector fields is characterized as structurally stable; this class corresponds to the class of Morse-Smale vector fields on closed manifolds, studied by Palis, Peixoto Smale, and others. In this class, new phenomena occur as saddle connections along the boundary of M which are persistent by small perturbations. Thus, the techniques introduced by J. Palis (Topology 8 (1969)), which inspired the proof of the stability of a vector field in such a class, were substantially changed. Such modifications represent a main difficulty in extending our results to higher dimensions