Strong anomaly in diffusion generated by iterated maps

We investigate the diffusion generated deterministically by periodic iterated maps that are defined by x(1+1) = x(t) + ax(t)(z) exp[-(b/x(t))(z-1)], z > 1. It is shown that the obtained mean squared displacement grows asymptotically as sigma(2)(t) similar to ln(l/(z-1))(t) and that the corresponding propagator decays exponentially with the scaling variable \ x \/root sigma(2)(t). This strong diffusional anomaly stems from the anomalously bread distribution of waiting times in the corresponding random walk process and leads to a behavior obtained for diffusion in the presence of random local fields. A scaling approach is introduced which connects the explicit form of the maps to the mean squared displacement.