  We show, using generic globally-coupled systems, that the collective dynamics
of large chaotic systems is encoded in their Lyapunov spectra: most modes are
typically localized on a few degrees of freedom, but some are delocalized,
acting collectively on the trajectory. For globally-coupled maps, we show
moreover 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.
