Mixing properties of set-valued maps on hyperspaces via Furstenberg families☆
Mixing properties of set-valued maps on hyperspaces via Furstenberg families☆
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DOI：
10.1016/j.chaos.2012.01.003
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发表时间：
2012-04
影响因子：
7.8
通讯作者：
Heman Fu;Zhitao Xing
中科院分区：
文献类型：
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作者：
Heman Fu;Zhitao Xing
设X是度量空间，f是X的连续自映射.在K（X）上，X的所有非空紧子集的集合，f通过令f <$（K）=f（K）自然地导出连续映射f <$，其中K∈K（X）。在这篇论文中，Furstenberg族被大量地用于研究f的混合性质和f ′的混合性质之间的关系。因此，我们得到了一些一般性的结论，推广了Banks [Chaos for induced hypersspace maps，Chaos Solitons & Fractals 2005; 25（3）：681-685.]，Kwietniak和Oprocha [诱导超空间映射的拓扑熵和混沌，混沌孤子与分形2007; 33：76-86.].
Let X be a metric space and f be a continuous self-map of X. On K(X), the set of all nonempty compact subsets of X, f induces a continuous map f¯ naturally by letting f¯(K)=f(K) for K∈K(X). In this paper Furstenberg families are heavily used to investigate the relationships between mixing properties of f and those of f¯. Consequently, several general conclusions are developed, which extent the results of Banks [Chaos for induced hyperspace maps, Chaos Solitons & Fractals 2005; 25(3):681–685.], Kwietniak and Oprocha [Topological entropy and chaos for induced hyperspace maps, Chaos Solitons & Fractals 2007; 33:76–86.].