Closed characteristics on non-compact hypersurfaces in $${\mathbb {R}^{2n}}$$

Viterbo demonstrated that any (2n − 1)-dimensional compact hypersurface of contact type has at least one closed characteristic. This result proved the Weinstein conjecture for the standard symplectic space (, ω). Various extensions of this theorem have been obtained since, all for compact hypersurfaces. In this paper we consider non-compact hypersurfaces coming from mechanical Hamiltonians, and prove an analogue of Viterbo’s result. The main result provides a strong connection between the top half homology groups H _i (M), i = n, . . . , 2n − 1, and the existence of closed characteristics in the non-compact case (including the compact case). J. B. van den Berg is supported by NWO VENI grant 639.031.204. R. C. Vandervorst and F. Pasquotto are supported by NWO VIDI grant 639.032.202. This research is also partially supported by the RTN project ‘Fronts-Singularities’.