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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.06047 |
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Table of Contents:
- In this article, we exhibit certain linking properties of periodic orbits of $C^{1+α}$ flows with positive topological entropy on closed 3-manifolds M. It is shown that any such flow contains a link L of periodic orbits and a horseshoe K in MŁ, such that all periodic orbits in K are unique in their homotopy class in MŁ(among periodic orbits in M). Moreover, the entropy of the flow 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.