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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2308.06047 |
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| _version_ | 1866910306736799744 |
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| author | Meiwes, Matthias |
| author_facet | Meiwes, Matthias |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06047 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological entropy and orbit growth in link complements Meiwes, Matthias Dynamical Systems Symplectic Geometry 37B10, 37C10, 53D42 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. |
| title | Topological entropy and orbit growth in link complements |
| topic | Dynamical Systems Symplectic Geometry 37B10, 37C10, 53D42 |
| url | https://arxiv.org/abs/2308.06047 |