  We analyze the properties of a Lennard-Jones system at the level of the
potential energy landscape. After an exhaustive investigation of the
topological features of the landscape of the systems, obtained studying small
size sample, we describe the dynamics of the systems in the multi-dimensional
configurational space by a simple model. This consider the configurational
space as a connected network of minima where the dynamics proceeds by jumps
described by an appropriate master equation. Using this model we are able to
reproduce the long time dynamics and the low temperature regime. We investigate
both the equilibrium regime and the off-equilibrium one, finding those typical
glassy behavior usually observed in the experiments such as: {\it i)} stretched
exponential relaxation, {\it ii)} temperature-dependent stretching parameter,
{\it iii)} breakdown of the Stokes-Einstein relation, and {\it iv)} appearance
of a critical temperature below which one observes deviation from the
fluctuation-dissipation relation as consequence of the lack of equilibrium in
the system.
