  We consider quantum maps induced by periodically-kicked scattering systems
and discuss the computation of their resonance spectra in terms of complex
scaling and sufficiently weak absorbing potentials. We also show that strong
absorptive and projective openings, as commonly used for open quantum maps,
fail to produce the resonance spectra of kicked scattering systems, even if the
opening does not affect the classical trapped set. The results are illustrated
for a concrete model system whose dynamics resembles key features of ionization
and exhibits a trapped set which is organized by a topological horseshoe at
large kick strength. Our findings should be useful for future tests of fractal
Weyl conjectures and investigations of dynamical tunneling.
