  The universal nature of black hole collapse in asymptotically $AdS_3$
gravitational theories suggests that its holographic dual process,
thermalization, should similarly be fixed by the universal features of 2d CFT
with large central charge $c$. It is known that non-equilibrium states with
scaling dimensions of order $c$ can be sorted into states that eventually
thermalize and those that fail to do so. By proving an equivalence between
bounded Virasoro coadjoint orbits and certain (in)stability intervals of Hill's
equation it is shown that a state that fails to thermalize can be promoted to a
thermalizing state by preparing the system beforehand with an energy greater
than an appropriate threshold energy. It is generally a difficult problem to
ascertain whether a state will thermalize or not. As partial progress to this
problem a set of lower bounds are presented for the treshold energy, which can
alternatively be interpreted as criteria for thermalization.
