Morse-Smale vector fields on 4-manifolds with boundary. (English) Zbl 0632.58023

Larbarca, R.; Pacifico, M. J.

Dynamical systems and bifurcation theory, Proc. Meet., Rio de Janeiro/Braz. 1985, Pitman Res. Notes Math. Ser. 160, 215-275 (1987).

[For the entire collection see Zbl 0621.00019.]
The authors give a definition and a characterization of Morse-Smale vector fields on four-manifolds with boundary. Surprisingly, there are some vector fields which are stable in this case but are not stable in the boundaryless case. Thus, this paper shows that the theory of Morse- Smale vector fields on manifolds with boundary may not be developed simply through a straightforward modification of the corresponding boundaryless case.

MSC:

37D15

Morse-Smale systems

Keywords:

characterization of Morse-Smale vector fields on four-manifolds with boundary