  The concept of A-coupled-expanding map, which is one of the more natural and
useful ideas generalized the horseshoe map, is well known as a criterion of
chaos. It is well known that distributional chaos is one of the concepts which
reflect strong chaotic behaviour. In this paper, we focus the relations between
A-coupled-expanding and distributional chaos. We prove two theorems that give
sufficient conditions for a strictly A-coupled-expanding map to be
distributionally chaotic in the senses of two kinds, where A is an irreducible
transition matrix.
