Visually building Smale flows in \(S^3\) (Q1578881)

The article is concerned with the realization of simple Smale flows on the 3-sphere. By definition, a single Smale flow possesses three basis sets: an attractor, a repeller, which are closed orbits, and a nontrivial saddle set which might even be chaotic. Using template theory several ways to construct Smale flows are illustrated. In particular, for any given knot there is a Smale flow which has a periodic orbit of this knot type as the saddle set.