Knotting Minimal Sets

Alex Clark; John Hunton

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arXiv · 2509.17133

Knotting Minimal Sets

Alex Clark·John Hunton

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Abstract

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.

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Alex Clark, John Hunton. 2025-09-21. Knotting Minimal Sets. https://arxiv.org/abs/2509.17133

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