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EQUALITY OF KOLMOGOROV-SINAI AND PERMUTATION ENTROPY FOR ONE-DIMENSIONAL MAPS CONSISTING OF COUNTABLY MANY MONOTONE PARTS

机译:KOLMOGOOROV-SINAI和排列熵的平等,用于一维地图,包括多种单调零件

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摘要

In this paper, we show that, under some technical assumptions, the Kolmogorov-Sinai entropy and the permutation entropy are equal for one-dimensional maps if there exists a countable partition of the domain of definition into intervals such that the considered map is monotone on each of those intervals. This is a generalization of a result by Bandt, Pompe and G. Keller, who showed that the above holds true under the additional assumptions that the number of intervals on which the map is monotone is finite and that the map is continuous on each of those intervals.
机译:在本文中,我们表明,如果在某些技术假设下,Kolmogorov-Sinai熵和置换熵等于一维映射,如果定义域的可数分区分为间隔,则认为所考虑的地图是单调的每个间隔。这是Bandt,Pompe和G. Keller的结果的概括,该概念在额外的假设下表明上面的额外假设是正确的,即地图是单调的间隔数是有限的,并且地图在每一个上连续间隔。

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