The Godbillon-Vey Invariant as a Restricted Casimir of Three-dimensional Ideal Fluids

Abstract

We show the Godbillon-Vey invariant arises as a `restricted Casimir' invariant for three-dimensional ideal fluids associated to a foliation. We compare to a finite-dimensional system, the rattleback, where analogous phenomena occur.

arXiv comment8 pages

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Cited by in corpus (2)

• The Godbillon-Vey Invariant as Topological Vorticity Compression and Obstruction to Steady Flow in Ideal Fluids
• A geometric look at MHD and the Braginsky dynamo