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Smooth autonomous fast dynamo action on the three-torus
We construct a nonempty $C^k$-open family, for some $k\in\mathbb{N}$, of smooth, autonomous, divergence-free velocity fields on $\mathbb{T}^3$ that generate fast dynamos. This resolves the Fast Dynamo Conjecture of Zeldovich and Sakharov, as recorded in Arnold's book of problems. We first construct
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