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In this paper we consider Hausdorff dimension of the sets of Li-Yorke pairsfor some chaotic dynamical systems including $A$-coupled expanding systems. Weprove that Li-Yorke pairs of $A$- coupled-expanding system under someconditions have full hausdorff dimension on the invariant set. we generalizethe result of [8] on the Hausdorff dimension of Li-Yorke pairs of dynamicalsystems topologically conjugate to the full shift and having a self-similarinvariant set to the case of dynamical system conjugated to some kind ofsubshifts. And Hausdorff dimension of "chaotic invariant set" for some kind ofA-coupled-expanding maps is shown.

Hausdorff dimension of the sets of Li-Yorke pairs for some chaotic dynamical systems including A-coupled expanding systems