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Dense invariant open distributionally scrambled sets and closed distributionally scrambled sets

机译：密不变量开放分布加扰集和封闭分布加扰集

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摘要

It is known that in a compact dynamical system, the whole space can be a Li-Yorke scrambled set, but this does not hold for distributional chaos. In this paper we prove that the complement of a distributionally scrambled set must be an infinite set. Then we give an example of an uncountable dense invariant open extremal distributionally scrambled set which is the complement of a countable infinite set. This presents one kind of the "largest" (from the topological point of view) distributionally scrambled set in a compact dynamical system. Moreover, we construct an uncountable closed distributionally scrambled set.
机译：众所周知，在一个紧凑的动力学系统中，整个空间可以是一个Li-Yorke扰动的集合，但是这对于分布混乱并不成立。在本文中，我们证明了分布加扰集的补码必须是无限集。然后我们给出一个不可数的稠密不变开放极值分布扰动集的例子，它是可数无限集的补集。这表示了紧凑动力系统中一种“最大”（从拓扑学角度来看）分布加扰集。此外，我们构造了一个不可数的封闭分布加扰集。

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  • 来源
    《Topology and its applications》 |2014年第15期|110-120|共11页
  • 作者

    Hui Wang; Fengchun Lei; Lidong Wang;

  • 作者单位

    School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;

    School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;

    Department of Mathematics, Dalian Nationalities University, Dalian 116600, China,School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    Distributional chaos; Scrambled set;

    机译：分布混乱;炒锅;

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