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

A practical and popular technique to extract the symbolic dynamics from exp erimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized fur determining the symbols. We address to what extent the symbolic dynamics so obtained can faithfully re present the phase-space dynamics. Our principal result is that such a pract ice can lead to a severe misrepresentation of the dynamical system. The mea sured topological entropy is a Devil's staircase-like, but surprisingly non monotone, function of a parameter characterizing the amount of misplacement of the partition.