Periodicity as condition to noise robustness for chaotic maps with piecewise constant invariant density

Chaotic maps represent an effective method of generating random-like sequences, that combines the benefits of relying on simple, causal models with good unpredictability. However, since chaotic maps behavior is generally strongly dependent on unavoidable implementation errors and external perturbations, the possibility of guaranteeing map statistical robustness is of great practical concern. Here we present a technique to guarantee the independence of the first-order statistics of external perturbations, modeled as an additive, map-independent random variable. The developed criterion applies to a quite general class of maps.