Integrals of motion: Evolution of our simulated clusters in the integrals of motion (IOM) space, in particular, the E × L_Z diagram. Their positions in this diagram are scattered in a sequential colour-map, starting from the same point in light grey at t = 0, and ending in darker tones (green for globular clusters originally formed in dark matter mini-halos, and red for clusters devoid of dark matter). The last snapshot is marked by a cross, for each cluster. This plot highlights a bimodal evolutionary distribution of clusters originally embedded in dark matter (moving towards lower energies) and those who were not (moving only slightly towards higher energies), and more importantly, it shows that clusters originally embedded in dark matter move significantly in IOM space, such that their association with past merger events through this diagram is not reliable.