  A network of $N$ elements is studied in terms of a deterministic globally
coupled map which can be chaotic. There exists a range of values for the
parameters of the map where the number of different macroscopic configurations
is very large, and there is violation of selfaveraging. The time averages of
functions, which depend on a single element, computed over a time $T$, have
probability distributions that do not collapse to a delta function, for
increasing $T$ and $N$. This happens for both chaotic and regular motion, i.e.
positive or negative Lyapunov exponent.
