  We argued in arXiv:1408.0624 that the quartic scalar field in AdS has
features that could be instructive for answering the gravitational stability
question of AdS. Indeed, the conserved charges identified there have recently
been observed in the full gravity theory as well. In this paper, we continue
our investigation of the scalar field in AdS and provide evidence that in the
Two-Time Formalism (TTF), even for initial conditions that are far from
quasi-periodicity, the energy in the higher modes at late times is
exponentially suppressed in the mode number. Based on this and some related
observations, we argue that there is no thermalization in the scalar TTF model
within time-scales that go as $\sim 1/\epsilon^2$, where $\epsilon$ measures
the initial amplitude (with only low-lying modes excited). It is tempting to
speculate that the result holds also for AdS collapse.
