  This paper concentrates on optical Hamiltonian systems of $T*\T^n$, i.e.
those for which $\Hpp$ is a positive definite matrix, and their relationship
with symplectic twist maps. We present theorems of decomposition by symplectic
twist maps and existence of periodic orbits for these systems. The novelty of
these results resides in the fact that no explicit asymptotic condition is
imposed on the system. We also present a theorem of suspension by Hamiltonian
systems for the class of symplectic twist map that emerges in our study.
Finally, we extend our results to manifolds of negative curvature.
