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.
Original language | English |
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Article number | 154103 |
Number of pages | 4 |
Journal | Physical Review Letters |
Volume | 103 |
Issue number | 15 |
DOIs | |
Publication status | Published - 9 Oct 2009 |
Keywords
- globally coupled maps
- characteristic exponents
- large numbers
- limit
- oscillators
- law