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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.17133 |
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| _version_ | 1866914126035419136 |
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| author | Clark, Alex Hunton, John |
| author_facet | Clark, Alex Hunton, John |
| contents | We consider the ways minimal sets of flows in $S^3$ may be embedded. We prove that given any $C^2$ flow on $S^3$ with positive entropy, there is an uncountable collection $\mathcal{M}$ of topologically distinct minimal sets such that for each $M\in \mathcal{M}$ there are infinitely many embedded copies of $M$ in the flow, each copy with a distinct knot type, thus extending work of Franks and Williams for periodic orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Knotting Minimal Sets Clark, Alex Hunton, John Dynamical Systems 37C10, 57K12 (Primary) 37B10, 37B35, 37B52 (Secondary) We consider the ways minimal sets of flows in $S^3$ may be embedded. We prove that given any $C^2$ flow on $S^3$ with positive entropy, there is an uncountable collection $\mathcal{M}$ of topologically distinct minimal sets such that for each $M\in \mathcal{M}$ there are infinitely many embedded copies of $M$ in the flow, each copy with a distinct knot type, thus extending work of Franks and Williams for periodic orbits. |
| title | Knotting Minimal Sets |
| topic | Dynamical Systems 37C10, 57K12 (Primary) 37B10, 37B35, 37B52 (Secondary) |
| url | https://arxiv.org/abs/2509.17133 |