Structural stability of vector fields on 3-manifolds with boundary (Q801196)

From 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, Smale, Peixoto 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 \textit{J. Palis} [Topology 8, 385-405 (1969; Zbl 0189.239)], 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.