  We present a numerical study of rotational dynamics in AdS$_5$ with equal
angular momenta in the presence of a complex doublet scalar field. We determine
that the endpoint of gravitational collapse is a Myers-Perry black hole for
high energies and a hairy black hole for low energies. We investigate the
timescale for collapse at low energies $E$, keeping the angular momenta
$J\propto E$ in AdS length units. We find that the inclusion of angular momenta
delays the collapse time, but retains a $t\sim1/E$ scaling. We perturb and
evolve rotating boson stars, and find that boson stars near AdS appear stable,
but those sufficiently far from AdS are unstable. We find that the dynamics of
the boson star instability depend on the perturbation, resulting either in
collapse to a Myers-Perry black hole, or development towards a stable
oscillating solution.
