Closed Magnetic Geodesics on $S^2$

TL;DR

This paper proves the existence of simple closed curves with specific geodesic curvature on the 2-sphere, relating to periodic magnetic orbits, expanding understanding of magnetic geodesics.

Contribution

It provides new existence results for magnetic geodesics on the sphere, linking geometric curves to physical magnetic orbit models.

Findings

Existence of closed magnetic geodesics on $S^2$ established.

Characterization of geodesic curvature conditions for closed curves.

Connection between geometric curves and magnetic field dynamics.

Abstract

We give existence results for simple closed curves with prescribed geodesic curvature on $S^{2}$, which correspond to periodic orbits of a charge in a magnetic field.