Finite intersection property and dynamical compactness
Finite intersection property and dynamical compactness
复制标题
有限交集性质和动力紧致性
DOI：
10.1007/s10884-017-9600-8
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发表时间：
2018
影响因子：
1.3
通讯作者：
Zhang Guohua
中科院分区：
文献类型：
--
作者：
Huang Wen;Khilko Danylo;Kolyada Sergii;Peris Alfred;Zhang Guohua
作为动力系统混沌的一个新概念，关于族的动力紧性在Huang等人中被引入和讨论。(J Different EQU 260(9)：6800-6827,2016)。在本文中，我们将继续研究这一概念。特别地，我们证明了所有动力系统关于一个Furstenberg族是动态紧的当且仅当这个族具有有限交性质。我们利用动力紧性的概念研究了弱混合和弱不交。我们还进一步探讨了传递紧性与弱混合之间的区别。作为一个副产品，我们证明了一个点的-极限集和-极限集可能具有完全不同的拓扑结构。在此基础上，建立了极小系统的多重灵敏度、灵敏度紧性和传递灵敏度的等价关系。最后，这些概念也在线性动力学的背景下进行了探索。
Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in Huang et al. (J Differ Equ 260(9):6800–6827, 2016). In this paper we continue to investigate this notion. In particular, we prove that all dynamical systems are dynamically compact with respect to a Furstenberg family if and only if this family has the finite intersection property. We investigate weak mixing and weak disjointness by using the concept of dynamical compactness. We also explore further difference between transitive compactness and weak mixing. As a byproduct, we show that the-limit and the-limit sets of a point may have quite different topological structure. Moreover, the equivalence between multi-sensitivity, sensitive compactness and transitive sensitivity is established for a minimal system. Finally, these notions are also explored in the context of linear dynamics.