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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Science China Press

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10.1016/j.apsusc.2011.10.044

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1869-1862

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Distributionally scrambled set and minimal set

Authors: LiDong Wang Hui Wang
Publish Date: 2013/09/17
Volume: 57, Issue: 9, Pages: 1953-1960
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Abstract

We investigate the relation between distributional chaos and minimal sets and discuss how to obtain various distributionally scrambled sets by using least and simplest minimal sets We show i an uncountable extremal distributionally scrambled set can appear in a system with just one simple minimal set a periodic orbit with period 2 ii an uncountable dense invariant distributionally scrambled set can occur in a system with just two minimal sets a fixed point and an infinite minimal set iii infinitely many minimal sets are necessary to generate a uniform invariant distributionally scrambled set and an uncountable dense extremal invariant distributionally scrambled set can be constructed by using just countably infinitely many periodic orbits

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