The Godbillon–Vey invariant as a restricted Casimir of three-dimensional ideal fluids*
Thomas Machon
Abstract
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.
Topics & Concepts
Invariant (physics)Ideal (ethics)PhysicsMathematicsCasimir effectMathematical physicsCovariant transformationPure mathematicsScaling dimensionInvariant polynomialQuantum Electrodynamics and Casimir EffectBlood properties and coagulationPhase Equilibria and Thermodynamics