  In this work, we analyze the necessary conditions for a nonlinear AdS-type
instability in the gravity-scalar field system. In particular, we discuss the
necessary conditions for a cascade of energy to higher modes by applying
results in KAM theory. Our analytical framework explains numerical observations
of instability of spacetimes even when the spectrum is only asymptotically
resonant, and the fact that a minimum field amplitude is needed to trigger it.
Our framework can be applied for similar stability analyses of fields in
(locally) asymptotically AdS spacetimes. We illustrate this with the example of
the AdS soliton. Further, we conjecture on the possible reasons for
quasi-periodic behaviour observed in perturbations of AdS spacetime. Certain
properties of the eigenfunctions of the linear system dictate whether there
will be localization in space leading to black hole formation. These properties
are examined using the asymptotics of Jacobi polynomials. Finally we discuss
recent results on the AdS instability in Einstein-Gauss-Bonnet gravity in light
of our work.
