Strong anomaly in diffusion generated by iterated maps

We investigate the diffusion generated deterministically by periodic iterated maps that are defined by x_t+1 = x_t+ax^z_texp[−(b/x_t)^z−1], z > 1. It is shown that the obtained mean squared displacement grows asymptotically as ²(t)∼ln^1/(z−1)(t) and that the corresponding propagator decays exponentially with the scaling variable |x|/√σ²(t). This strong diffusional anomaly stems from the anomalously broad 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.