The Lusternik–Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

Asselle Luca, Benedetti Gabriele

Abstract

Let M be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian H:T*M → ℝ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if M is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of H.