Deterministic Brownian Motion: The Effects of Perturbing a Dynamical System by a Chaotic Semi-Dynamical System
Michael C. Mackey, Marta Tyran-Kaminska
Abstract
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.
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