  We revisit the issues of non-linear AdS stability, its relation to growing
(secular) terms in naive perturbation theory around the AdS background, and the
need and possible strategies for resumming such terms. To this end, we review a
powerful and elegant resummation method, which is mathematically identical to
the standard renormalization group treatment of ultraviolet divergences in
perturbative quantum field theory. We apply this method to non-linear
gravitational perturbation theory in the AdS background at first non-trivial
order and display the detailed structure of the emerging renormalization flow
equations. We prove, in particular, that a majority of secular terms (and the
corresponding terms in the renormalization flow equations) that could be
present on general grounds given the spectrum of frequencies of linear AdS
perturbations, do not in fact arise.
