Instabilities and nonstatistical behavior in globally coupled systems

The mean field in a globally coupled system of chaotic logistic maps does not obey the standard rules of statistics, even for systems of very large sizes. This indicates the existence of intrinsic instabilities in its evolution. Here these instabilities are related to the very non-smooth behavior of mean values in a single logistic map, as a function of its parameter. Problems of this kind do not affect a similar system of coupled tent maps, where good statistical behavior has been found. We also explore the transition between these two regimes. (author). 15 refs, 9 figs