On distributionally chaotic and null systems
On distributionally chaotic and null systems
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DOI：
10.1016/j.jmaa.2010.08.068
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发表时间：
2011-03
影响因子：
1.3
通讯作者：
Heman Fu;J. Xiong;Feng Tan
中科院分区：
文献类型：
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作者：
Heman Fu;J. Xiong;Feng Tan
By a topological dynamical system, we mean a pair (X,f), where X is a compactum and f is a continuous self-map on X. A system is said to be null if its topological sequence entropies are zero along all strictly increasing sequences of natural numbers. We show that there exists a null system which is distributionally chaotic. This system admits open distributionally scrambled sets, and its collection of all maximal distributionally scrambled sets has the same cardinality as the collection of all subsets of the phase space. Finally such system can even exist on continua.
