Abstract
In this paper, some properties of a strictly A A -coupled-expanding map in compact subsets of a metric space are studied, where A A is a transition matrix. It is shown that this map has a compact invariant set on which it is topologically semi-conjugate to the subshift for A A . If the subshift for A A has positive topological entropy, then the map is chaotic in the sense of Li-Yorke. Moreover, in the one-dimensional case, the map is at most two-to-one conjugate to the subshift for A A and chaotic in the sense of Devaney.
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