Statistical properties of one-dimensional chaotic signals

Signals arising out of nonlinear dynamical systems are compelling models for a wide range of phenomena. We develop several properties of signals obtained from Markov maps, an important family of such systems, and present analytical techniques for computing their statistics. Among other results, we demonstrate that all Markov maps produce signals with rational spectra, and can therefore be viewed as “chaotic ARMA processes”. Finally, we demonstrate how Markov maps can approximate to arbitrary precision any of a broad class of chaotic maps and their statistics