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

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

2000-05-19

arxiv.org/abs/nlin/0005040v1

Phys. Rev. Lett. 85, 3524-3527 (2000)

Nonlinear Sciences

Chaotic Dynamics

8 pages + 4 figures in .pdf

Scientific paper

10.1103/PhysRevLett.85.3524

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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