title: Lyapunov analysis captures the collective dynamics of large chaotic systems.
abstract: 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.
authors.affiliation: Service de Physique de l'Etat Condensé, CEA-Saclay, 91191 Gif-sur-Yvette, France.
authors.forename: Kazumasa A
authors.initials: KA
authors.lastname: Takeuchi
authors.forename: Francesco
authors.initials: F
authors.lastname: Ginelli
authors.forename: Hugues
authors.initials: H
authors.lastname: Chaté