  We examine the phase diagram of a Bose-Einstein condensate of atoms,
interacting with an attractive pseudopotential, in a quadratic-plus-quartic
potential trap rotating at a given rate. Investigating the behavior of the gas
as a function of interaction strength and rotational frequency of the trap, we
find that the phase diagram has three distinct phases, one with vortex
excitation, one with center of mass excitation, and an unstable phase in which
the gas collapses.
