Sporadic randomness: The transition from the stationary to the nonstationary condition - art. no. 026210

We address the study of sporadic randomness by means of the Manneville map. We point out that the Manneville map is the generator of fluctuations yiel ding the Levy processes, and that these processes are currently regarded by some authors as statistical manifestations of a nonextensive form of therm odynamics. For this reason we study the sensitivity to initial conditions w ith the help of a nonextensive form of the Lyapunov coefficient. The purpos e of this research is twofold. The former is to assess whether a finite dif fusion coefficient might emerge from the nonextensive approach. This proper ty, at first sight, seems to be plausible in the nonstationary case, where conventional Kolmogorov-Sinai analysis predicts a vanishing Lyapunov coeffi cient. The latter purpose is to confirm or reject conjectures about the non extensive nature of Levy processes. We find that the adoption of a nonexten sive approach does not serve any predictive purpose: It does not even signa l a transition from a stationary to a nonstationary regime. These conclusio ns are reached by means of both numerical and analytical calculations that shed light on why the Levy processes do not imply any need to depart from t he adoption of traditional complexity measures.