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.