Closed characteristics on non - compact hypersurfaces in R 2 n Jan

Viterbo demonstrated that any (2n − 1)-dimensional compact hypersurface M ⊂ (R2n, ω) of contact type has at least one closed characteristic. This result proved the Weinstein conjecture for the standard symplectic space (R2n, ω). Various extensions of this theorem have been obtained since, all for compact hypersurfaces. In this paper we consider non-compact hypersurfaces M ⊂ (R2n, ω) 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 Hi (M), i = n, . . . , 2n − 1, and the existence of closed characteristics in the non-compact case (including the compact case).