Infinitely many periodic orbits in non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level

TL;DR

This paper proves that on surfaces with genus at least two, for almost every low energy level, there are infinitely many closed magnetic geodesics under oscillating non-exact magnetic fields.

Contribution

It establishes the existence of infinitely many periodic orbits for almost all low energy levels in a new setting involving non-exact oscillating magnetic fields on higher genus surfaces.

Findings

Infinitely many closed magnetic geodesics exist for almost every low energy level.

Results apply to surfaces with genus at least two.

The energy levels considered are below a specific critical value.

Abstract

In this paper we consider oscillating non-exact magnetic fields on surfaces with genus at least two and show that for almost every energy level $k$ below a certain value $\tau_+^*(g,\sigma)$ less than or equal to the "Ma\~n\'e critical value of the universal cover" there are infinitely many closed magnetic geodesics with energy $k$.