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arXiv · 1602.04745

Helicity is the only integral invariant of volume-preserving transformations

Alberto Enciso·Daniel Peralta-Salas·Francisco Torres de Lizaur
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Abstract

We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional $\mathcal I$ defined on exact divergence-free vector fields of class $C^1$ on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that $\mathcal I$ is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity.

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Alberto Enciso, Daniel Peralta-Salas, Francisco Torres de Lizaur. 2016-02-15. Helicity is the only integral invariant of volume-preserving transformations. https://doi.org/10.1073/pnas.1516213113

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