Phys. Rev. Lett. 103, 154103 (2009) [4 pages]Lyapunov Analysis Captures the Collective Dynamics of Large Chaotic SystemsReceived 24 July 2009; published 9 October 2009 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. © 2009 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.103.154103
DOI:
10.1103/PhysRevLett.103.154103
PACS:
05.45.−a, 05.70.Ln, 05.90.+m
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