  Coupled oscillators, even identical ones, display a wide range of behaviours,
among them synchrony and incoherence. The 2002 discovery of so-called chimera
states, states of coexisting synchronized and unsynchronized oscillators,
provided a possible link between the two and definitely showed that different
parts of the same ensemble can sustain qualitatively different forms of motion.
Here, we demonstrate that globally coupled identical oscillators can express a
range of coexistence patterns more comprehensive than chimeras. A hierarchy of
such states evolves from the fully synchronized solution in a series of
cluster-splittings. At the far end of this hierarchy, the states further
collide with their own mirror-images in phase space -- rendering the motion
chaotic, destroying some of the clusters and thereby producing even more
intricate coexistence patterns. A sequence of such attractor collisions can
ultimately lead to full incoherence of only single asynchronous oscillators.
Chimera states, with one large synchronized cluster and else only single
oscillators, are found to be just one step in this transition from low- to
high-dimensional dynamics.
