In this article, we exhibit certain linking properties of periodic orbits of \(C^{1+\alpha }\) flows with positive topological entropy on closed 3-manifolds M. It is shown that any such flow \(\varphi \) contains a link \(\mathcal {L}\) of periodic orbits and a horseshoe K in \(M{\setminus } \mathcal {L}\) , such that all periodic orbits in K are unique in their homotopy class in \(M{\setminus } \mathcal {L}\) (among periodic orbits in M). Moreover, the entropy of \(\varphi \) can be approximated by the entropies of such horseshoes K. A version of that result for chords is obtained. Our main motivation comes from Reeb dynamics, and, as an application, we address a question by Alves–Pirnapasov and obtain that the topological entropy of a 3-dimensional, \(C^{\infty }\) -generic Reeb flow can be approximated by the exponential homotopical growth rates of contact homology in link complements.
