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A non-PI minimal system is Li-Yorke sensitive


Authors: Song Shao and Xiangdong Ye
Journal: Proc. Amer. Math. Soc. 146 (2018), 1105-1112
MSC (2010): Primary 37B05; Secondary 54H20
DOI: https://doi.org/10.1090/proc/13779
Published electronically: September 14, 2017
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Abstract: It is shown that any non-PI minimal system is Li-Yorke sensitive. Consequently, any minimal system with non-trivial weakly mixing factor (such a system is non-PI) is Li-Yorke sensitive, which answers affirmatively an open question by Akin and Kolyada in [Nonlinearity, 16 (2003) pp. 1421-1433].


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Song Shao
Affiliation: Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
Email: songshao@ustc.edu.cn

Xiangdong Ye
Affiliation: Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
Email: yexd@ustc.edu.cn

DOI: https://doi.org/10.1090/proc/13779
Received by editor(s): January 12, 2017
Received by editor(s) in revised form: April 13, 2017
Published electronically: September 14, 2017
Additional Notes: This research was supported by NNSF of China (11571335, 11371339, 11431012) and by “the Fundamental Research Funds for the Central Universities”.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society

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