Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level

TL;DR

This paper proves that for almost every energy level below a critical value, an exact magnetic flow on a surface has infinitely many periodic orbits, advancing understanding of magnetic dynamical systems.

Contribution

It establishes the existence of infinitely many periodic orbits for almost all subcritical energy levels in exact magnetic flows on surfaces, a significant extension of prior results.

Findings

Infinitely many periodic orbits exist for almost every subcritical energy level.

The result applies to exact magnetic flows on closed surfaces.

It covers energy levels below the Mañé critical value of the universal cover.

Abstract

We consider an exact magnetic flow on the tangent bundle of a closed surface. We prove that for almost every energy level $\kappa$ below the Ma\~n\'e critical value of the universal cover there are infinitely many periodic orbits with energy $\kappa$.