Abstract
A topological dynamical system is n-sensitive, if there is a positive constant such that in each non-empty open subset there are n distinct points whose iterates will be apart from the constant at least for a same moment. The properties of n-sensitivity in minimal systems are investigated. It turns out that a minimal system is n-sensitive if and only if the n-th regionally proximal relation Q n contains a point whose coordinates are pairwise distinct. Moreover, the structure of a minimal system which is n-sensitive but not (n + 1)-sensitive (n ⩾ 2) is determined.
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This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10501042, 10531010) and the Ministry of Education of China (Grant No. 20050358053)
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Shao, S., Ye, X. & Zhang, R. Sensitivity and regionally proximal relation in minimal systems. Sci. China Ser. A-Math. 51, 987–994 (2008). https://doi.org/10.1007/s11425-008-0012-4
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DOI: https://doi.org/10.1007/s11425-008-0012-4