Tensor function analysis of quantized chaotic piecewise-affine pseudo-Markov systems. II. Higher order correlations and self-similarity

For pt. I see ibid., vol. 49, pp. 137-49 (2002).The general approach developed in the companion paper for the statistical analysis of trajectories produced by a class of chaotic systems generalizing the classical view of piecewise-affine Markov maps is here applied to the computation of higher order correlations. For any given order m, a procedure is given to write a closed form expression in the z-transformed domain for the mth dimensional tensor encoding the contribution of the system dynamics to the correlation functions of that order. After having defined and discussed a suitable generalization of the concept of second-order self-similarity, we finally use this general procedure to show that simple chaotic maps may exhibit highly nontrivial behaviors also in their higher order statistics.