  Since horizon formation in global anti-de Sitter spacetime is dual to
thermalization of a conformal field theory on a compact space, whether generic
initial data is stable or unstable against gravitational collapse is of great
interest. We argue that all the known stable initial data for massless scalars
are dominated by single scalar eigenmodes, specifically providing strong
numerical evidence consistent with the interpretation that initial data with
equal energies in two modes collapse on time scales of order the inverse square
of the amplitude. We further scan the parameter space for massive scalar field
initial data and present evidence for a novel class of stable or quasi-stable
solutions for massive scalars with energy spread through several eigenmodes.
