REMARK ON METRIC ANALYSIS OF RECONSTRUCTED DYNAMICS FROM CHAOTIC TIME-SERIES

We show that, for finite chaotic time series, the embedding with the delay time which corresponds to a reconstructed phase diagram similar to the original one does not necessarily lead to a good convergence of the correlation dimension. Delay time influences the measures of reconstructed dynamics besides the geometries of reconstructed phase diagrams. Moreover, the plateau onset of correlation dimension and the maximal Lyapunov exponent can be produced by the low-dimensional embedding of the dynamics.