Some properties of coupled-expanding maps in compact sets

In this paper, some properties of a strictly A-coupled-expanding map in compact subsets of a metric space are studied, where 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. If the subshift for 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 and chaotic in the sense of Devaney. © 2012 American Mathematical Society.