Abstract
In this paper, the notions of periodic point are compared, and the sensitivity of semigroup actions on Hausdorff uniform spaces is studied. We show that for an action of a semigroup on a compact uniform space, if it is syndetically transitive and not minimal, then it is syndetically sensitive. We point out that if an action of a semigroup on a uniform space (does not need to be compact) is topologically transitive, not minimal, and has a dense set of s-periodic points, then it is syndetically sensitive. Additionally, we prove that if an action of a monoid on a uniform space (does not need to be compact) is topologically transitive, not minimal, and has a dense set of FM-periodic points, then it is syndetically sensitive.
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The authors would like to thank the referees for the careful reading and many valuable comments.
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Supported by National Nature Science Funds of China (11471125, 11771149).
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Wang, H., Zhong, Y. A Note on Sensitivity in Uniform Spaces. J Dyn Control Syst 24, 625–633 (2018). https://doi.org/10.1007/s10883-017-9375-6
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DOI: https://doi.org/10.1007/s10883-017-9375-6