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Auslander-Yorke type dichotomy theorems for stronger versions of $ r$-sensitivity


Authors: Kairan Liu and Xiaomin Zhou
Journal: Proc. Amer. Math. Soc. 147 (2019), 2609-2617
MSC (2010): Primary 37B05; Secondary 54H20
DOI: https://doi.org/10.1090/proc/14435
Published electronically: February 20, 2019
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Abstract: In this paper, for $ r\in \mathbb{N}$ with $ r\geq 2$ we consider several stronger versions of $ r$-sensitivity and measure-theoretical $ r$-sensitivities by analyzing subsets of non-negative integers, for which the $ r$-sensitivity occurs. We obtain an Auslander-Yorke type dichotomy theorem: a minimal topological dynamical system is either thickly $ r$-sensitive or an almost $ m$-to-one extension of its maximal equicontinuous factor for some $ m\in \{1,\cdots , r-1\}$.


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Additional Information

Kairan Liu
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
Email: lkr111@mail.ustc.edu.cn

Xiaomin Zhou
Affiliation: Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People’s Republic of China
Email: zxm12@mail.ustc.edu.cn

DOI: https://doi.org/10.1090/proc/14435
Keywords: Sensitivity, measurable sensitivity, almost finite-to-one extension
Received by editor(s): August 11, 2018
Received by editor(s) in revised form: September 25, 2018
Published electronically: February 20, 2019
Additional Notes: The second author was partially supported by NSFC(11801193).
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society