CORRELATIONS AND DYNAMICS IN ENSEMBLES OF MAPS - SIMPLE-MODELS

Interesting correlations between individual maps have been reported in systems of globally coupled maps and of uncoupled maps submitted to a global noise. These have been described under the heading ''violation of the law of large numbers.'' An elementary explanation of this phenomenon is proposed. It is illustrated in a simple approximation for logistic maps. We then introduce an alternative model of coupled homographic maps which is much easier to study. A precise analysis of the emergent collective dynamics is given.