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 mag where the number of different macroscopic configurations N(N) is very large, N(N) similar to exp root 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.