The main result asserts the existence of noncontractible periodic orbits for compactly supported time-dependent Hamiltonian systems on the unit cotangent bundle of the torus or of a negatively curved manifold whenever the generating Hamiltonian is sufficiently large over the zero section. The proof is based on Floer homology and on the notion of a relative symplectic capacity. Applications include results about propagation properties of sequential Hamiltonian systems, periodic orbits on hypersurfaces, Hamiltonian circle actions, and smooth Lagrangian skeletons in Stein manifolds.
Paul Biran. Leonid Polterovich. Dietmar Salamon. "Propagation in Hamiltonian dynamics and relative symplectic homology." Duke Math. J. 119 (1) 65 - 118, 15 July 2003. https://doi.org/10.1215/S0012-7094-03-11913-4