  We study multifractal properties in the spectrum of effective
time-independent Hamiltonians obtained using a perturbative method for a class
of delta-kicked systems. The evolution operator in the time-dependent problem
is factorized into an initial kick, an evolution dictated by a time-independent
Hamiltonian, and a final kick. We have used the double kicked $SU(2)$ system
and the kicked Harper model to study butterfly spectrum in the corresponding
effective Hamiltonians. We have obtained a generic class of $SU(2)$
Hamiltonians showing self-similar spectrum. The statistics of the generalized
fractal dimension is studied for a quantitative characterization of the
spectra.
