  In this paper we consider Hausdorff dimension of the sets of Li-Yorke pairs
for some chaotic dynamical systems including $A$-coupled expanding systems. We
prove that Li-Yorke pairs of $A$- coupled-expanding system under some
conditions have full hausdorff dimension on the invariant set. we generalize
the result of [8] on the Hausdorff dimension of Li-Yorke pairs of dynamical
systems topologically conjugate to the full shift and having a self-similar
invariant set to the case of dynamical system conjugated to some kind of
subshifts. And Hausdorff dimension of "chaotic invariant set" for some kind of
A-coupled-expanding maps is shown.
