Topological Conjugacy Propagates Stochastic Robustness of Chaotic Maps (Special Section on Nonlinear Theory and Its Applications)

We here consider an extension of the validity of classical criteria ensuring the robustness of the statistical features of discrete time dynamical systems with respect to implementation inaccuracies and noise. The result is achieved by proving that, whenever a discrete time dynamical system is robust, all the discrete time dynamical systems topologically conjugate with it are also robust. In particular, this result offer an explanation for the stochastic robustness of the logistic map, which is confirmed by the reported experimental measurements.