Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series
Chaotic Dynamics
2009-10-31 v1
Abstract
A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for determining the symbols. We address to what extent the symbolic dynamics so obtained can faithfully represent the phase-space dynamics. Our principal result is that such practice leads to a severe misrepresentation of the dynamical system. The measured topological entropy is a Devil's staircase-like, but surprisingly nonmonotone, function of a parameter characterizing the amount of misplacement of the partition.
Keywords
Cite
@article{arxiv.nlin/0005040,
title = {Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series},
author = {Erik M. Bollt and Theodore Stanford and Ying-Cheng Lai and Karol Zyczkowski},
journal= {arXiv preprint arXiv:nlin/0005040},
year = {2009}
}
Comments
8 pages + 4 figures in .pdf