周期吸附系统的分布混沌

由一个紧致度量空间X以及连续映射f:X→X所组成的偶对(X,f)称之为一个动力系统.若存在f的不动点p以及另一周期点q,使得对于任一非空开集U(?)X,都有∪_(n=0)~∞f~n(U)含有p和q,则称(X,f)是一个周期吸附系统,其中f~i表示f的i次迭代.本文指出:若(X,f)是一个周期吸附系统并且X是自密的,则存在一个f的分布混沌集D,使得D与每一非空开集之交都包含着一个Cantor集.

Distributional Chaos Of Periodically Adsorbing System

By a dynamical system $(X, f)$ we mean a compact metric space $X$ together with a continuous map $f: X\to X$. A dynamical system $(X,f)$ is called a periodically adsorbing system if there exist a fixed point $p$ and a periodic point $q\ne p$ of $f$ such that for any nonempty open set $U\subset X$, the set $\bigcup_{n=1}^\infty f^n(U)$ contains both $p$ and $q$, where $f^i$ is the $i$th iteration of $f$. It turns out that if $(X,f)$ is a periodically adsorbing system and $X$ is perfect, then there exists a distributional chaotic set $D$ of $f$ such that the intersection of $D$ and any nonempty open set contains a Cantor set.