Strange chaotic triangular maps

We show that in the class TT of the triangular maps (x,y)↦(f(x),gx(y)) of the square there is a map with zero topological entropy which is Li-Yorke chaotic on a minimal set, but not distributionally chaotic DC2  . This result answers an open question concerning classification of maps in TT with zero topological entropy, and contributes to an old problem formulated by Sharkovsky.