TY - JOUR

T1 - Equality of Kolmogorov-sinai and permutation entropy for one-dimensional maps consisting of countably many monotone parts

AU - Gutjahr, Tim

AU - Keller, Karsten

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85065797955&partnerID=8YFLogxK

U2 - 10.3934/dcds.2019170

DO - 10.3934/dcds.2019170

M3 - Journal articles

AN - SCOPUS:85065797955

SN - 1078-0947

VL - 39

SP - 4207

EP - 4224

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 7

ER -