Smale flows on ${\mathbb{S}}^2\times {\mathbb{S}}^1$

Abstract

In this paper, we use abstract Lyapunov graphs as a combinatorial tool to obtain a complete classification of Smale flows on ${\mathbb{S}}^2\times {\mathbb{S}}^1$. This classification gives necessary and sufficient conditions that must be satisfied by an abstract Lyapunov graph in order for it to be associated to a Smale flow on ${\mathbb{S}}^2\times {\mathbb{S}}^1$.