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

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