  In their celebrated "Period three implies chaos" paper, Li and Yorke proved
that if a continuous interval map f has a period 3 point then there is an
uncountable scrambled set S on which f has very complicated dynamics. One
question arises naturally: Can this set S be chosen invariant under f? The
answer is positive for turbulent maps and negative otherwise. In this note, we
shall use symbolic dynamics to achieve our goal. In particular, we obtain that
the tent map T(x) = 1 - |2x-1| on [0, 1] has a dense uncountable invariant
1-scrambled set which consists of transitive points.
