The trunkenness of a volume-preserving vector field

Ana Rechtman (1) , Pierre Dehornoy (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 IF - Institut Fourier

We construct a new invariant—the trunkenness—for volume-perserving vector fields on S^3 up to volume-preserving diffeomorphism. We prove that the trunkenness is independent from the helicity and that it is the limit of a knot invariant (called the trunk) computed on long pieces of orbits.

Mots clés: vector field; Euler equation; knot; invariant

Domaines: Systèmes dynamiques [math.DS]; Topologie géométrique [math.GT]; Dynamique des Fluides [physics.flu-dyn]; Physique des plasmas [physics.plasm-ph]; Astrophysique stellaire et solaire [astro-ph.SR]

Ana Rechtman, Pierre Dehornoy. The trunkenness of a volume-preserving vector field. 2016. ⟨hal-01326696v1⟩