Simple Smale flows and their templates on S3

The embedded template is a geometric tool in dynamics being used to model knots and links as periodic orbits of $3$-dimensional flows. We prove that for an $S^3$ with fixed homeomorphism type, its boundary trivalent spatial graph complete isotopic invariant. Moreover, we construct invariant templates by Kauffman's graphs, which set links. As application, the classification simple Smale flows on discussed.