In this talk we discuss some ways to detect periodic orbits of autonomous Hamiltonian flows on non-compact regular hypersurfaces. A first task that is already delicate in this setting is to produce bounded orbits of such flows. Fix a Hamiltonian H : M → R with M symplectic but non-compact and let γH be the gradient flow of H with respect to some Riemannian metric on M and let XH be the Hamiltonian flow of H. The key idea is to translate certain algebraic topological properties of an index pair (in the sense of the Conley index) (N1, N0) of an isolated invariant set of γH into recurrence properties of XH. It is useful to note that such index pairs (N1, N0) are reasonably easy to construct for gradient flows. When H is generic our results show that if the relative homology H∗(N1, N0; Z) has torsion or if a certain differential in the Ω fr ∗ (ΩM)- Atiyah-Hirzebruch-Serre spectral sequence associated to the fibration induced over the pair (N1, N0) from the path loop fibration ΩM → PM → M does not vanish, then XH has some non-trivial periodic orbits (Ωfr ∗ (ΩM) is the framed bordism ring of the pointed loop space of M, ΩM).