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, by varying the parameters in the Hamiltonian cyclically with a period T and thus inducing suitable geometric phases in the states, fractional revivals can be eliminated at the relevant times T, 2T,.... Further, with the introduction of this time step T, the occurrence of near full revivals can be mapped onto that of Poincare recurrences in an irrational rotation map of the circle. The distinctive recurrence statistics of the latter can thus serve as a clear signature of the dynamics of wave packet revivals.