Statistical approach to discrete-time chaotic systems: advanced tools for quantized chaotic trajectories

Abstract

Classical tools for statistical analysis of chaotic maps can be generalized to express any-order joint probability of the state and thus any-order correlation functions of the trajectories. When trajectories are quantized correlations can be naturally expressed as combinations of tensors. These expressions feature noteworthy properties when,. piecewise-affine Markov maps are considered. The class of (n,t)-tailed shifts spans the range of maps producing exponentially vanishing correlation and allows the derivation of an analytical expression for any-order quantized correlation functions.