  We propose damage spreading (DS) as a tool to investigate the topological
features related to the ruggedness of the free energy landscape. We argue that
DS measures the positiveness of the largest Lyapunov exponent associated to the
basins of attraction visited by the system during its dynamical evolution. We
discuss recent results obtained in the framework of mode-coupling theory and
comment how to extend them to the study of realistic glasses. Preliminary
results are presented for purely repulsive soft-sphere glasses.
