Broken Ergodicity and Glassy Behavior in a Deterministic Chaotic Map

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 $N(N)$ is very large, N(N)~exp√c(a)N, and there is violation of self-averaging. The time averages of functions, which depend on a single element, computed over a time T, have probability distributions that for any N do not collapse to a delta function, for increasing T. This happens for both chaotic and regular motion, i.e., positive or negative Lyapunov exponent.