# American Institute of Mathematical Sciences

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July  2019, 39(7): 4207-4224. doi: 10.3934/dcds.2019170

## Equality of Kolmogorov-Sinai and permutation entropy for one-dimensional maps consisting of countably many monotone parts

 Institut für Mathematik, Ratzeburger Allee 160, D-23562 Lübeck, Germany

* Corresponding author: Tim Gutjahr

Received  October 2018 Revised  February 2019 Published  April 2019

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.

Citation: Tim Gutjahr, Karsten Keller. Equality of Kolmogorov-Sinai and permutation entropy for one-dimensional maps consisting of countably many monotone parts. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 4207-4224. doi: 10.3934/dcds.2019170
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##### References:
Graph of the Gauss function T
The striped area corresponds to the set $R = \{(\omega_1, \omega_2)\in\Omega^2|~\omega_1\leq \omega_2\}$ and the gray area to $(T\times T)^{-1}(R)$ for the Gauss function $T$
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