Quantization of Periodic Hamiltonian Orbits

We give a rigorous and complete definition of the Maslov index of periodic Hamiltonian orbits. Our definition makes use of the properties of the Maslov indices on the metaplectic group that we have studied in a former work (1992). Our theory is definitive in the sense that it contains those of Sugita and of Creagh, Littlejohn et al. as particular cases.