The trunkenness of a volume-preserving vector field

TL;DR

This paper introduces a new invariant called trunkenness for volume-preserving vector fields on S^3, demonstrating its independence from helicity and its relation to knot invariants, enriching the understanding of dynamical systems.

Contribution

The paper constructs the trunkenness invariant for volume-preserving vector fields and establishes its properties and relation to existing invariants.

Findings

Trunkenness is independent of helicity.

Trunkenness is the limit of the knot invariant called trunk.

The invariant applies to volume-preserving vector fields on S^3.

Abstract

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.