  A powerful tool is developed for the characterization of chaotic signals. The
approach is based on the symbolic encoding of time series (according to their
ordinal patterns) combined with the ensuing characterization of the
corresponding cylinder sets. Quantitative estimates of the Kolmogorov-Sinai
entropy are obtained by introducing a modified permutation entropy which takes
into account the average width of the cylinder sets. The method works also in
hyperchaotic systems and allows estimating the fractal dimension of the
underlying attractors.
