  Wave packets in a system governed by a Hamiltonian with a generic nonlinear
spectrum typically exhibit both full and fractional revivals. It is shown that
the latter can be eliminated by inducing suitable geometric phases in the
states, by varying the parameters in the Hamiltonian cyclically with a period
T. Further, with the introduction of this natural time step T, the occurrence
of near revivals can be mapped onto that of Poincar\'{e} recurrences in an
irrational rotation map of the circle. The distinctive recurrence time
statistics of the latter can thus serve as a clear signature of the dynamics of
wave packet revivals.
