Contact topology and hydrodynamics III: knotted orbits

Etnyre, John; Ghrist, Robert

doi:10.1090/S0002-9947-00-02651-9

Contact topology and hydrodynamics III: knotted orbits
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by John Etnyre and Robert Ghrist PDF

Trans. Amer. Math. Soc. 352 (2000), 5781-5794 Request permission

Abstract:

We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct a steady nonsingular solution to the Euler equations on a Riemannian $S^3$ whose flowlines trace out closed curves of all possible knot and link types. Using careful contact-topological controls, we can make such vector fields real-analytic and transverse to the tight contact structure on $S^3$. Sufficient review of concepts is included to make this paper independent of the previous works in this series.

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