Entropy of interval maps via permutations

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Order Patterns in Time Series (2007, background): “It turned out that for trajectories of chaotic dynamical systems, permutation entropy agrees with the usual metric entropy (Bandt et al. 2002; Amig o et al., 2005) .”
A survey of consecutive patterns in permutations (2015, methodology): “utive pattern containment: if p 2Allow(f) and p contains s, then s 2Allow(f) [30]. This property allows us to apply combinatorial tools to the study of dynamical systems. For example, it was shown in [11] that for a piecewise monotone map f, the limit lim n!¥ jAllow(f)\S nj1=n (8) 14 Sergi Elizalde ”
TIME SERIES FROM THE ORDINAL VIEWPOINT (2007, methodology): “Note that the result of Bandt et al. [ 3 ] can be used for estimating the”
Permutation entropy: A nonlinear statistical measure for status characterization of rotary machines (2012, background): “Furthermore, an overview on both theory and applications of permutation entropy is introduced in [27] in detail, and with more and more researchers have devoted to this topic, more theoretical insights on permutation entropy can be seen in [28–30].”
Ordinal time series analysis (2005, background): “In Bandt et al. (2002) we proved that for arbitrary piecewise monotone one-dimensional maps, lim n→∞ hn exists and equals the well-known Kolmogorov–Sinai entropy of the map.”