Infinitely many noncontractible closed magnetic geodesics on non-compact manifolds

TL;DR

This paper investigates the existence and multiplicity of periodic magnetic geodesics on non-compact manifolds using Morse theory, focusing on energy levels above a critical value.

Contribution

It provides new results on the existence and multiplicity of magnetic geodesics on non-compact manifolds at high energy levels.

Findings

Existence of infinitely many noncontractible magnetic geodesics

Multiplicities of periodic orbits established

Application of Morse theory to non-compact settings

Abstract

In this paper we study the existence and multiplicity of periodic orbits of exact magnetic flows with energy levels above the Ma\~{n}\'{e} critical value of the universal cover on a non-compact manifold from the viewpoint of Morse theory.