相对破碎家庭敏感性

IF 0.8 3区 数学 Q2 MATHEMATICS
Zhuo Wei Liu, Tao Yu
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引用次数: 0

摘要

让 π: (X, T) → (Y, S) 是两个拓扑动力系统之间的因子映射,而 \(\cal{F}\) 是ℤ的弗斯滕伯格族。我们引入相对破损的 \(\cal{F}\) 敏感性概念。让 \(\cal{F}_{s}\) (resp. \(\cal{F}_{text\{pubd}},\cal{F}_{text{inf}}\)) 是由所有联合子集(resp. positive upper Banach density subsets, infinite subsets)组成的族。我们证明,对于因子映射 π:(X,T) → (Y,S) 之间,π 对于 \(\cal{F}=\cal{F}_{s}\) 或 \(\cal{F}_{text{pubd}}\) 是相对破碎的(\cal{F}\)-敏感的,当且仅当存在一个相对敏感对,它是(Rπ,T(2))的一个(\(\cal{F}\)-循环点;是相对破碎的(\cal{F}_{text{inf}})敏感的,当且仅当存在一个不渐近的相对敏感对时。对于极小系统间的因子映射 π:(X,T)→(Y,S),我们通过因子映射到它的最大等连续因子得到相对破碎(\cal{F}\)-敏感的结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Relative Broken Family Sensitivity

Let π: (X, T) → (Y, S) be a factor map between two topological dynamical systems, and \(\cal{F}\) a Furstenberg family of ℤ. We introduce the notion of relative broken \(\cal{F}\)-sensitivity. Let \(\cal{F}_{s}\) (resp. \(\cal{F}_{\text{pubd}},\cal{F}_{\text{inf}}\)) be the families consisting of all syndetic subsets (resp. positive upper Banach density subsets, infinite subsets). We show that for a factor map π: (X, T) → (Y, S) between transitive systems, π is relatively broken \(\cal{F}\)-sensitive for \(\cal{F}=\cal{F}_{s}\) or \(\cal{F}_{\text{pubd}}\) if and only if there exists a relative sensitive pair which is an \(\cal{F}\)-recurrent point of (Rπ, T(2)); is relatively broken \(\cal{F}_{\text{inf}}\)-sensitive if and only if there exists a relative sensitive pair which is not asymptotic. For a factor map π: (X, T) → (Y, S) between minimal systems, we get the structure of relative broken \(\cal{F}\)-sensitivity by the factor map to its maximal equicontinuous factor.

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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
138
审稿时长
14.5 months
期刊介绍: Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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