  In this paper we generalize the dynamical systems analysis of the cubic
galileon model previously investigated in \cite{rtgui} by including
self-interaction potentials beyond the exponential one. It will be shown that,
consistently with the results of \cite{rtgui}, the cubic self-interaction of
the galileon vacuum appreciably modifies the late-time cosmic dynamics by the
existence of a phantom-like attractor (among other super-accelerated solutions
that are not of interest in the present investigation). In contrast, in the
presence of background matter the late-time cosmic dynamics remains practically
the same as in the standard quintessence scenario. This means that we can not
recover the cubic galileon vacuum continuously from the more general cubic
quintessence with background matter, by setting to zero the matter energy
density (and the pressure). This happens to be a kind of cosmological vDVZ
discontinuity that can be evaded by means of the cosmological version of the
Vainshtein screening mechanism.
