We apply renormalized entropy as a complexity measure to the logistic and
sine-circle maps. In the case of logistic map, renormalized entropy decreases
(increases) until the accumulation point (after the accumulation point up to
the most chaotic state) as a sign of increasing (decreasing) degree of order in
all the investigated periodic windows, namely, period-2, 3, and 5, thereby
proving the robustness of this complexity measure. This observed change in the
renormalized entropy is adequate, since the bifurcations are exhibited before
the accumulation point, after which the band-merging, in opposition to the
bifurcations, is exhibited. In addition to the precise detection of the
accumulation points in all these windows, it is shown that the renormalized
entropy can detect the self-similar windows in the chaotic regime by exhibiting
abrupt changes in its values. Regarding the sine-circle map, we observe that
the renormalized entropy detects also the quasi-periodic regimes by showing
oscillatory behavior particularly in these regimes. Moreover, the oscillatory
regime of the renormalized entropy corresponds to a larger interval of the
nonlinearity parameter of the sine-circle map as the value of the frequency
ratio parameter reaches the critical value, at which the winding ratio attains
the golden mean.Comment: 14 pages, 7 figure
