Pei Xing, Dolan Kevin, Moss Frank, Lai Ying-Cheng
Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121.
Chaos. 1998 Dec;8(4):853-860. doi: 10.1063/1.166371.
The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise. (c) 1998 American Institute of Physics.
