  We present a mapping of potentially chaotic time-dependent quantum kicked
systems to an equivalent effective time-independent scenario, whereby the
system is rendered integrable. The time-evolution is factorized into an initial
kick, followed by an evolution dictated by a time-independent Hamiltonian and a
final kick. This method is applied to the kicked top model. The effective
time-independent Hamiltonian thus obtained, does not suffer from spurious
divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is
used. The quasienergy spectrum of the Floquet operator is found to be in
excellent agreement with the energy levels of the effective Hamiltonian for a
wide range of system parameters. The density of states for the effective system
exhibits sharp peak-like features, pointing towards quantum criticality. The
dynamics in the classical limit of the integrable effective Hamiltonian shows
remarkable agreement with the non-integrable map corresponding to the actual
time-dependent system in the non-chaotic regime. This suggests that the
effective Hamiltonian serves as a substitute for the actual system in the
non-chaotic regime at both the quantum and classical level.
