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Published in:
05-09-2017
A Note on Sensitivity in Uniform Spaces
Published in: Journal of Dynamical and Control Systems | Issue 4/2018
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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.