Topological Permutation Entropy
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Permutation entropy, as conventional entropy, comes in the metric version (Chap. 6) and in the topological version (this chapter). Topological permutation entropy was also introduced by Bandt et al.  , together with metric permutation entropy. Let us stress once more that the concept of metric permutation entropy of a map introduced in the last chapter differs from the original one, the difference consisting basically in the order of an iterated limit (first the length of the orbit, then the precision of the measurement, as in the definition of the Kolmogorov–Sinai entropy). This technical change made possible to generalize one of the main results of , namely, the equality of metric entropy and metric permutation entropy for piecewise monotone maps on one-dimensional intervals to higher dimensions at the expense of requiring ergodicity (Theorem 10).
KeywordsTopological Entropy Symbolic Dynamic Oriented Graph Outgrowth Ratio Permutation Entropy
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