Furstenberg family and chaos
Furstenberg family and chaos
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DOI：
10.1007/s11425-007-0052-1
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
J. Xiong;Jie Lü;Feng Tan
中科院分区：
文献类型：
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作者：
J. Xiong;Jie Lü;Feng Tan
Furstenberg族是由向上遗传的正整数集合的一些子集组成的族，即A∧BandA∈implyB∈。对于给定系统（即具有完备度量空间和空间连续自映射的一对）和Furstenberg族，给出了空间中点的置乱对的定义，将Li-Yorke意义上的置乱对和分布意义上的置乱对分别对应于合适的Furstenberg族。本文研究了系统的置乱对集的基本性质。定义了一般混沌系统和一般强混沌系统。给出了一类一般强混沌系统的判据。
A Furstenberg familyis a family, consisting of some subsets of the set of positive integers, which is hereditary upwards, i.e.A⊂BandA∈implyB∈. For a given system (i.e., a pair of a complete metric space and a continuous self-map of the space) and for a Furstenberg family, the definition of-scrambled pairs of points in the space has been given, which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be-scrambled pairs corresponding respectively to suitable Furstenberg family. In the present paper we explore the basic properties of the set of-scrambled pairs of a system. The generically-chaotic system and the generically strongly-chaotic system are defined. A criterion for a generically strongly-chaotic system is showed.