Dispersion of the Arnold's asymptotic ergodic Hopf invariant and a formula for its calculation

TL;DR

This paper explores the dispersion of Arnold's asymptotic ergodic Hopf invariant in magnetic fields and provides a formula for its calculation, with potential applications in turbulent magnetic field analysis.

Contribution

It introduces a new formula for calculating Arnold's ergodic Hopf invariant and discusses its dispersion in magnetic fields, expanding understanding of magnetic topology in turbulence.

Findings

Derived a formula for the Hopf invariant calculation

Illustrated the dispersion behavior in magnetic fields

Suggested applications in turbulent magnetic field analysis

Abstract

The paper contains an example to describe magnetic fields in a conductive medium. The authors assume that new applications for turbulent magnetic fields in the case the magnetic field is not left- and right- polarized are possible.