Every 3-manifold admits a structurally stable nonsingular flow with three basic sets

Abstract

This paper is devoted to proving that every closed orientable 3 3 -manifold admits a simple Smale flow X t X_t . Here a simple Smale flow is a structurally stable nonsingular flow whose chain recurrent set is composed of a periodic orbit attractor, a periodic orbit repeller and a transitive saddle invariant set, i.e., a saddle basic set.