We consider the sensitivity from a topological point of view. We show that a continuous, topologically transitive and non-minimal action of a monoid S on an infinite $$T_4$$ topological space which admits a dense set of almost periodic points is sensitive. We also prove that a uniformly continuous, topologically transitive and non-minimal action of a monoid S on an infinite Hausdorff uniform space which admits a dense set of almost periodic points is thickly syndetically sensitive. We point out that if a continuous action of an Abelian group on a compact metric space is chaotic in the sense of Devaney and has a fixed point, then for every positive integer $$n\ge 2$$, it is Li–Yorke n–$$\varepsilon $$-chaotic for some $$\varepsilon >0$$. Moreover, we show that a continuous and transitive compact action of a semigroup S on a compact metric space is Li–Yorke sensitive and Li–Yorke $$\varepsilon $$-chaotic for some $$\varepsilon >0$$.

中文翻译：

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灵敏度、德瓦尼混沌和 Li–Yorke $$\varepsilon $$ε-chaos

我们从拓扑的角度考虑灵敏度。我们表明，幺半群 S 在无限的 $$T_4$$ 拓扑空间上的连续、拓扑传递和非最小动作是敏感的。我们还证明了幺半群 S 在无限豪斯多夫均匀空间上的一致连续、拓扑传递和非最小作用，该空间允许一组密集的几乎周期性的点，这是高度合合敏感的。我们指出，如果一个阿贝尔群在紧致度量空间上的连续动作在德瓦尼意义上是混沌的并且有一个不动点，那么对于每个正整数 $$n\ge 2$$，它是 Li-Yorke n –$$\varepsilon $$-对于某些 $$\varepsilon >0$$ 来说是混乱的。而且，