【摘要】 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^∞fⁿ（U）含有p和q,则称（X,f）是一个周期吸附系统,其中fⁱ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.更多还原

【Abstract】 By a dynamical system （X,f） we mean a compact metric space X together with a continuous map f:X→X.A dynamical system （X,f） is called a periodically adsorbing system if there exist a fixed point p and a periodic point q≠p of f such that for any nonempty open set U（?）X,the set∪_n=1^∞fⁿ（U） contains both p and q, where fⁱ is the ith 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.更多还原