Figure 2.

(a) Absolute value of trajectory positions x_t, t = 0,1,… , for the logistic map f_μ(x) at μ_∞, with initial condition x₀ = 0, in logarithmic scale as a function of the logarithm of the time t, also shown by the numbers close to the points. The arrows indicate the distances equivalent to the principal diameters $d_{n,0}$. (b) The positions |x_t| of the trajectory in (a) at selected iteration times t = 2ⁿ − 1 (black dots) reproduced by Eq. (14) with α = 1.7555 (red). The inset shows the same data plotted in ${\ln }_{{\alpha }^{\prime }}{p}_k/p_{\min }$ scale, $p_k=1/\left|x_k\right|$, p_min = 1 and α^′ = 0.2445. The straight line evidences the (time) extensivity of the entropy in Eq. (13). See text for description.