  The event-by-event correlations between three flow amplitudes are measured
for the first time in Pb--Pb collisions, using higher-order Symmetric
Cumulants. We find that different three-harmonic correlations develop during
the collective evolution of the medium, when compared with correlations that
exist in the initial state. These new results cannot be interpreted in terms of
previous lower-order flow measurements, since contributions from two-harmonic
correlations are explicitly removed in the new observables. Comparison with
Monte Carlo simulations provides new and independent constraints for the
initial conditions and system properties of nuclear matter created in heavy-ion
collisions.
