Deterministic Brownian motion: The effects of perturbing a dynamical system by a chaotic semi-dynamical system

Here we review and extend central limit theorems for chaotic deterministic semi-dynamical discrete time systems. We then apply these results to show how Brownian motion-like behavior can be recovered and how an Ornstein–Uhlenbeck process can be constructed within a totally deterministic framework. These results illustrate that under certain circumstances the contamination of experimental data by “noise” may be alternately interpreted as the signature of an underlying chaotic process.