Deterministic Brownian Motion: The Effects of Perturbing a Dynamical System by a Chaotic Semi-Dynamical System

Details Deterministic Brownian Motion: The Effects of Perturbing a Dynamical System by a Chaotic Semi-Dynamical System Deterministic Brownian Motion: The Effects of Perturbing a Dynamical System by a Chaotic Semi-Dynamical System

2004-08-13

arxiv.org/abs/cond-mat/0408330v1

Phys. Rep. 422 (2006), no. 5, 167--222

Physics

Condensed Matter

Statistical Mechanics

65 pages, 8 figures

Scientific paper

10.1016/j.physrep.2005.09.002

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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