Analogues of Auslander-Yorke theorems for multi-sensitivity
Analogues of Auslander-Yorke theorems for multi-sensitivity
复制标题
多敏感性 Auslander-Yorke 定理的类似物
DOI：
10.1017/etds.2016.48
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发表时间：
2018
影响因子：
0.9
通讯作者：
Zhang Guohua
中科院分区：
文献类型：
--
作者：
Huang Wen;Kolyada Sergii;Zhang Guohua
研究紧度量空间上连续满射自映射的多灵敏度和厚灵敏度问题。我们的主要结果表明，一个最小系统要么是多敏感的，要么是它的最大等连续因子的几乎一一扩展。这与Auslander-Yorke二分定理类似：最小系统要么是敏感的，要么是等连续的。进一步，我们引入了综合等连续点的概念，并证明了传递系统要么是厚敏感的，要么是包含综合等连续点的，这是对Akin、Auslander和Berg另一个著名结果的改进。
We study multi-sensitivity and thick sensitivity for continuous surjective selfmaps on compact metric spaces. Our main result states that a minimal system is either multi-sensitive or an almost one-to-one extension of its maximal equicontinuous factor. This is an analog of the Auslander–Yorke dichotomy theorem: a minimal system is either sensitive or equicontinuous. Furthermore, we introduce the concept of a syndetically equicontinuous point, and we prove that a transitive system is either thickly sensitive or contains syndetically equicontinuous points, which is a refinement of another well-known result of Akin, Auslander and Berg.