Tensor function analysis of quantized chaotic piecewise-affine pseudo-Markov systems. I. Second-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 framework is based on a generalization of the Perron-Frobenius operator and on the mapping of its properties onto properties of tensor function algebra. The general results are specialized to the computation of second-order statistical behaviors and exemplified with the analysis of two nontrivial maps exhibiting self-similar correlation trends.