  In this paper we apply the tools of the dynamical systems theory in order to
uncover the whole asymptotic structure of the vacuum interactions of a galileon
model with a cubic derivative interaction term. It is shown that, contrary to
what occurs in the presence of background matter, the galileon interactions of
vacuum appreciably modify the late-time cosmic dynamics. In particular, a local
late-time attractor representing phantom behavior arises which is inevitably
associated with a big rip singularity. It seems that the gravitational
interactions of the background matter with the galileon screen the effects of
the gravitational self-interactions of the galileon, thus erasing any potential
modification of the late-time dynamics by the galileon vacuum processes. Unlike
other galileon models inspired in the DGP scenario, self-accelerating solutions
do not arise in this model.
