  For a real massless scalar field in general relativity with a negative
cosmological constant, we uncover a large class of spherically symmetric
initial conditions that are close to AdS, but whose numerical evolution does
not result in black hole formation. According to the AdS/CFT dictionary, these
bulk solutions are dual to states of a strongly interacting boundary CFT that
fail to thermalize at late times. Furthermore, as these states are not
stationary, they define dynamical CFT configurations that do not equilibrate.
We develop a two-timescale perturbative formalism that captures both direct and
inverse cascades of energy and agrees with our fully nonlinear evolutions in
the appropriate regime. We also show that this formalism admits a large class
of quasi-periodic solutions. Finally, we demonstrate a striking parallel
between the dynamics of AdS and the classic Fermi-Pasta-Ulam-Tsingou problem.
