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

Liu, Kairan; Zhou, Xiaomin

doi:10.1090/proc/14435

Auslander-Yorke type dichotomy theorems for stronger versions of $r$-sensitivity
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by Kairan Liu and Xiaomin Zhou PDF

Proc. Amer. Math. Soc. 147 (2019), 2609-2617 Request permission

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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