  Chaotic scattering in open Hamiltonian systems is a topic of fundamental
interest in physics, which has been mainly studied in the purely conservative
case. However, the effect of weak perturbations in this kind of systems has
been an important focus of interest in the last decade. In a previous work, the
authors studied the effects of a periodic forcing in the decay law of the
survival probability, and they characterized the global properties of escape
dynamics. In the present paper, we add two important issues in the effects of
periodic forcing: the fractal dimension of the set of singularities in the
scattering function, and the unpredictability of the exit basins, which is
estimated by using the concept of basin entropy. Both the fractal dimension and
the basin entropy exhibit a resonant-like decrease as the forcing frequency
increases. We provide a theoretical reasoning, which could justify this
decreasing in the fractality near the main resonant frequency, that appears for
$\omega \approx 1$. We attribute the decrease in the basin entropy to the
reduction of the area occupied by the KAM islands and the basin boundaries when
the frequency is close to the resonance. Finally, the decay rate of the
exponential decay law shows a minimum value of the amplitude, $A_c$, which
reflects the complete destruction of the KAM islands in the resonance. We
expect that this work could be potentially useful in research fields related to
chaotic Hamiltonian pumps, oscillations in chemical reactions and companion
galaxies, among others.
