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arXiv · 1904.03663

Relationship among several types of sensitivity in general semi-flows

Xinxing Wu·Xu Zhang
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Abstract

In this paper, we show that there exists a monoid, on which neither the syndetic property nor the dual syndetic property holds, and there exists a strongly mixing semi-flow with this monoid action which does not have thick sensitivity, syndetic sensitivity, thickly syndetic sensitivity, or thickly periodical sensitivity. Meanwhile, we show that there exists a thickly sensitive cascade which is not multi-sensitive. The first result answers positively Question 2, and the first and the second results answer negatively Question 3 in [A. Miller, A note about various types of sensitivity in general semiflows, Appl. Gen. Topol., 2018].

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Xinxing Wu, Xu Zhang. 2019-04-07. Relationship among several types of sensitivity in general semi-flows. https://arxiv.org/abs/1904.03663

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