  For a periodic Hamiltonian, periodic dynamical invariants may be used to
obtain non-degenerate cyclic states. This observation is generalized to the
degenerate cyclic states, and the relation between the periodic dynamical
invariants and the Floquet decompositions of the time-evolution operator is
elucidated. In particular, a necessary condition for the occurrence of cyclic
non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic
states are obtained for a magnetic dipole interacting with a precessing
magnetic field.
