Journal of Statistical Physics, Vol. 5, Nos. 5/6, 1988. p. 803-815.
We summarize recent arguments which show that for a broad class of classical, many-body dynamical model systems with short-range interactions (such as coupled maps, cellular automata, or partial differential equations), collectively chaotic states — nonstationary states wherein some Fourier amplitude varies chaotically in time - cannot occur generically. While chaos occurs ubiquitously on a local level in such systems, the macroscopic state of the system typically remains periodic or stationary...