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Figure 1: (a-c) Results for the baker map: a) The Lyapunov exponent as the analytic function of the parameter . b) The GP entropy rates estimated from 15 realizations of 16k time series (mean - thick line, mean SD - thin lines, coinciding with the mean) for different values of the parameter varying from 0.01 to 0.49 by step 0.005. c) Plot of GPER (the same line codes as in b) vs. LE. (d-f) Results for the Lorenz system: d) The positive Lyapunov exponents computed from the Lorenz equations for the parameter r varying from 33.75 to 65 by step 0.25. e) The GP entropy rates estimated from 15 realizations of 16k time series (mean - thick line, mean SD - thin lines) for different values of the parameter r varying as in plot d. f) Plot of GPER (the same line codes as before) vs. LE.

  
Figure 2: Results for the logistic map: a) The Lyapunov exponents computed from the map for the parameter a varying from 3.857 to 4 by step 0.001. b) The GP entropy rates estimated from 15 realizations of 16k time series (mean - thick line, mean SD - thin lines, coinciding with the mean) for different values of the parameter a varying as in plot a. c) Plot of GPER (the same line codes as before) vs. LE. Plots d, e, f: The same as the plots a, b, c, respectively, except of the parameter a varying by step 0.0003.

  
Figure 3: Further results for the Lorenz system: a) The positive Lyapunov exponents computed from the Lorenz equations for the parameter r varying from 33 to 120 by step 1. b) The GP entropy rates estimated from 15 realizations of 16k time series (mean - thick line, mean SD - thin lines, coinciding with the mean) for different values of the parameter r varying as in plot a. c) Plot of GPER (the same line codes as before) vs. LE. Plots d, e, f: The same as the plots a, b, c, respectively, except of the parameter r varying from 33 to 200 by step 1.

  
Figure: Standard deviation (square root of variance) of the GPER (a,c,e) and LE (b,d,f) estimates computed from the series generated by the logistic map after skipping zero (a,b), hundred thousand (c,d) and one billion (e,f) initial iterations to avoid influence of transients; plotted as the functions of the parameter a changing in the same range as in Fig. 2d-f.

  
Figure 5: Detailed illustration of one of the bifurcations of the logistic map. Lyapunov exponent (a), GP entropy rate (b,d,e), standard deviation of the GPER estimate (c) and standard deviation of the LE estimate (f); plotted as functions of the parameter a. Upper and lower parts of the plot b are zoomed in the plots d and e, respectively.