Existence of noncontractible periodic orbits of Hamiltonian systems separating two Lagrangian tori on T*Tn with application to nonconvex systems

In this paper, we show the existence of non-contractible periodic orbits in Hamiltonian systems defined on T*T-n separating two Lagrangian tori under a certain cone assumption. Our result gives a positive answer to a question of Polterovich in [P]. As an application, we find periodic orbits in almost all the homotopy classes on a dense set of energy levels in Lorentzian type mechanical Hamiltonian systems defined on T*T-2. This solves a problem of Arnold in [A].