Francesco Ginelli
"Lyapunov Analysis Captures the Collective Dynamics of Large Chaotic Systems"  We discuss collective dynamics in large chaotic systems. In particular, we show that the collective dynamics is encoded in the their Lyapunov spectrum and vectors. While most vectors are typically localized on a few degrees of freedom, a few are actually delocalized modes, acting collectively on the trajectory. Considering generic globally coupled maps, we establish a quantitative correspondence between the collective modes and some of the so-called Perron-Frobenius dynamics. Our results imply that the conventional definition of extensivity must be changed as soon as collective dynamics sets in.