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arXiv · 1509.08818

Analogues of Auslander-Yorke theorems for multi-sensitivity

Wen Huang·Sergii Kolyada·Guohua Zhang
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Abstract

In this paper we study multi-sensitivity and thick sensitivity for continuous surjective selfmaps on compact metric spaces. We show that multi-sensitivity implies thick sensitivity, and the converse holds true for transitive systems. Our main result is an analog of the Auslander-Yorke dichotomy theorem: a minimal system is either multi-sensitive or an almost one-to-one extension of its maximal equicontinuous factor. Furthermore, we refine it by introducing the concept of syndetically equicontinuous points: a transitive system is either thickly sensitive or contains syndetically equicontinuous points.

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Wen Huang, Sergii Kolyada, Guohua Zhang. 2015-09-29. Analogues of Auslander-Yorke theorems for multi-sensitivity. https://arxiv.org/abs/1509.08818

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