Optical Hamiltonians and symplectic twist maps

Abstract

This paper concentrates on optical Hamiltonian systems of T ∗ T n , i.e., those for which H pp 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.