@article{M2022, 
author = {Alqahtani Bushra Abdulshakoor M and Weibin Liu},
title = {Li-Yorke chaotic property of cookie-cutter systems},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {7},
pages = {13192-13207},
keywords = {cookie-cutter sets, mean Li-Yorke chaotic set, Hausdorff dimension, bounded distortion, Li-Yorke chaos},
url = {https://www.sciopen.com/article/10.3934/math.2022727},
doi = {10.3934/math.2022727},
abstract = {In this paper, we investigate mean Li-Yorke chaos along some sequence and Li-Yorke chaos for cookie-cutter systems. By applying bounded distortion and a locally    α-H                     o            ¨      lder condition, we show that the cookie-cutter set contains a mean Li-Yorke scrambled set along some sequence in which the Hausdorff dimension equals the Hausdorff dimension of the cookie-cutter set. That is to say, a cookie-cutter system is mean Li-Yorke chaotic along some sequence. Meanwhile, we proved that every mean Li-Yorke scrambled set is also a scrambled set; hence a cookie-cutter system is also Li-Yorke chaotic.}
}