| Sensitivity and regionally proximal relation in minimal systems |
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| 作者单位： | SHAO Song YE XiangDong ZHANG RuiFeng Department of Mathematics，University of Science and Technology of China，Hefei 230026，China |
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| 摘 要： | 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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Sensitivity and regionally proximal relation in minimal systems |
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| Authors: | Song Shao XiangDong Ye RuiFeng Zhang |
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| Institution: | SHAO Song YE XiangDong ZHANG RuiFeng Department of Mathematics,University of Science and Technology of China,Hefei 230026,China |
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| 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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| Keywords: | sensitivity n-sensitivity regionally proximal relation minimality |
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