Primitive links of non-singular Morse-Smale flows on the special Seifert fibered manifolds

Abstract

In this paper we consider a non-singular Morse-Smale flow Φ t on an irreducible, simple, closed, orientable 3-manifold M. We define a primitive flow ψ t from Φ t , and call the link type of the closed orbits of ψ t a primitive link of Φ t . We show that the link types of the primitive links are finite and every non-singular Morse-Smale flow on M is obtained from a primitive flow by exchanging the flow in a regular neighborhood of attracting or repelling closed orbits.