Figure 1

Illustration of the origin of the contributions to the second term in Eq. (5), for $n=4$ and $a=(\sqrt{5}-1)/3$.Reuse & Permissions

Figure 2

Cumulative probability distribution $F_n(x)$ for the twist map, Eq. (4) with $a=(\sqrt{5}-1)/3$. The upper curve corresponds to $n=4$ and the lower to $n=10$. Notice that in both cases the number of slope changes in $F_n(x)$ is equal to 3 as predicted by Eq. (5), whose positions are indicated in the figure by vertical dashed lines.Reuse & Permissions

Figure 3

(a) Probability density and (b) cumulative probability distribution for the tent map as obtained numerically using ${10}^6$ realizations. Dashed curves represent the prediction of the classical statistical theory of extremes. The irregular succession of plateaus in ${\rho }_{20}(x)$ and the increase of the slope of $F_{20}(x)$ in the final part of the interval are in full agreement with the general theory. The irregularity increases rapidly with the window (contrary to the quasiperiodic case), and there is no saturation and convergence to a smooth behavior in the limit of infinite window.Reuse & Permissions

Figure 4

As in Fig. 3 but for the cusp map. The irregularities pointed out in connection with Fig. 3 subsist, the main new point being the presence of a more appreciable probability mass in the left part of the interval.Reuse & Permissions