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Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series

Erik M. Bollt·Theodore Stanford·Ying-Cheng Lai·Karol Zyczkowski
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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.

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Erik M. Bollt, Theodore Stanford, Ying-Cheng Lai, Karol Zyczkowski. 2000-05-19. Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series. https://doi.org/10.1103/physrevlett.85.3524

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