Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series
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 a practice can lead 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.
Bollt
EM
Mathematics Department, 572 Holloway Road, U.S. Naval Academy, Annapolis, Maryland 21402-5002, USA.
Stanford
T
Lai
YC
Zyczkowski
K