Noise robustness condition for chaotic maps with piecewise constant invariant density

Chaotic maps represent an effective method for generating random-like sequences that combines the benefits of relying on simple, causal models with good unpredictability. Regrettably, such positive features are counterbalanced by the fact that statistics of true-implemented chaotic maps are generally strongly dependent on implementation errors and external perturbations. Here we study the effect of an external, additive, map-independent noise perturbation in the map model, and present a technique to guarantee, for a quite large class of maps, independence of the first-order statistics of the noise features.