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 highly chaotic but deterministic semi-dynamical discrete time systems. We then apply these results show how Brownian motion-like results are recovered, and how an Ornstein-Uhlenbeck process results within a totally deterministic framework. These results illustrate that the contamination of experimental data by "noise" may, under certain circumstances, be alternately interpreted as the signature of an underlying chaotic process. 
Michael C. Mackey, Marta Tyran-Kaminska