Periodicity and Quasi-Periodicity for Super-Integrable Hamiltonian   Systems
  Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a commensurability condition is imposed on an angular momentum component. 
Maurice Robert Kibler, Pavel Winternitz