Finite-type invariants of magnetic lines

Properties of magnetic flows are described using high dimensional configuration spaces. Arnold asymptotic ergodic invariant of magnetic lines is the basic example. Asymptotic invariants of magnetic lines are related to stable homotopy groups of spheres, are detected by Postnikov k-invariants. Anosov flows on 3D homology spheres are models of stable magnetic knots. Finite-type invariants of magnetic line are required to describe properties of turbulent flows and determine constraints in magnetic feld relaxation with free boundary.