Tensor Function Analysis of Quantized Chaotic Piecewise-Affine Pseudo-Markov Systems - Part I: 2nd Order Correlations and Self-Similarity

A general approach is developed for the statistical analysis of quantized trajectories produced by a class of chaotic maps generalizing piecewise-affine Markov systems. The frame- work is based on a generalization of the Perron–Frobenius oper- ator and on the mapping of its properties onto properties of tensor function algebra. The general results are specialized to the compu- tation of second-order statistical behaviors and exemplified with the analysis of two nontrivial maps exhibiting self-similar correla- tion trends.