2000/05/19 by Erik M. Bollt, Theodore Stanford, Ying-Cheng Lai +1 · 1 citation
Physics and Astronomy · #nlin.CD
paper · pdf · doi:10.1103/physrevlett.85.3524
published as Phys. Rev. Lett. 85, 3524-3527 (2000) · 8 pages + 4 figures in .pdf
arxiv created 2000/05/19 · arxiv updated 2009/11/30
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.