Tensor Function Analysis of Quantized Chaotic Piecewise-Affine Pseudo-Markov Systems - Part II: Higher Order Correlations and Self-Similarity

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 piece- wise-affine Markov maps is here applied to the computation of higher order correlations. For any given order , a procedure is given to write a closed form expression in the -transformed domain for the th 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 higly nontrivial behaviors also in their higher order statistics.