  The local density of states (LDOS) is a distribution that characterizes the
effect of perturbations on quantum systems. Recently, it was proposed a
semiclassical theory for the LDOS of chaotic billiards and maps. This theory
predicts that the LDOS is a Breit-Wigner distribution independent of the
perturbation strength and also gives a semiclassical expression for the LDOS
witdth. Here, we test the validity of such an approximation in quantum maps
varying the degree of chaoticity, the region in phase space where the
perturbation is applying and the intensity of the perturbation. We show that
for highly chaotic maps or strong perturbations the semiclassical theory of the
LDOS is accurate to describe the quantum distribution. Moreover, the width of
the LDOS is also well represented for its semiclassical expression in the case
of mixed classical dynamics.
