  We construct boson stars in global Anti de Sitter (AdS) space and study their
stability. Linear perturbation results suggest that the ground state along with
the first three excited state boson stars are stable. We evolve some of these
solutions and study their nonlinear stability in light of recent work
\cite{Bizon:2011gg} arguing that a weakly turbulent instability drives scalar
perturbations of AdS to black hole formation. However evolutions suggest that
boson stars are nonlinearly stable and immune to the instability for
sufficiently small perturbation. Furthermore, these studies find other families
of initial data which similarly avoid the instability for sufficiently weak
parameters. Heuristically, we argue that initial data families with widely
distributed mass-energy distort the spacetime sufficiently to oppose the
coherent amplification favored by the instability. From the dual CFT
perspective our findings suggest that there exist families of rather generic
initial conditions in strongly coupled CFT (with large number of degrees of
freedom) that do not thermalize in the infinite future.
