摘要
由一个紧致度量空间 以及连续映射 所组成的偶对
称之为一个动力系统. 若存在 的不动点 以及另一周期点
, 使得对于任一非空开集 , 都有 含有 和 , 则称 是一个周期吸附系统, 其中
表示 的 次迭代. 本文指出: 若
是一个周期吸附系统并且 是自密的, 则存在一个 的分布混沌集
, 使得 与每一非空开集之交都包含着一个 Cantor 集.
Abstract
By a dynamical system
we mean a compact metric space together with a
continuous map . A dynamical system is called
a periodically adsorbing system if there exist a fixed point
and a periodic point of such that for any
nonempty open set , the set contains both and , where is the th
iteration of . It turns out that if is a periodically
adsorbing system and is perfect, then there exists a
distributional chaotic set of such that the intersection
of and any nonempty open set contains a Cantor set.
关键词
分布混沌 /
周期吸附系统 /
动力系统
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吕杰熊金城谭
枫.
周期吸附系统的分布混沌. 数学学报, 2008, 51(6): 1109-111 https://doi.org/10.12386/A2008sxxb0129
Jie L\"UJin Cheng XIONGFeng TAN.
Distributional Chaos Of Periodically Adsorbing System. Acta Mathematica Sinica, Chinese Series, 2008, 51(6): 1109-111 https://doi.org/10.12386/A2008sxxb0129
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脚注
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