Properties of a chaotic invariant set of a dynamical system

alk

Can someone please explain to me,

why is it that having a dense set of periodic points is so important for an invariant set of a chaotic dynamical system?

It has something to do with exhibiting a regular behavior intermingled with the chaotic (the regular element according to Devaney), but I can't seem to find a way to conclude this line of thinking (I don't have Devaney's book right now).

Thanks in advance