Devaney’s definition has the virtues of being precise and compact. However, objections have been raised against it. Since the time he proposed his definition, it has been shown that (2) and (3) imply (1) if the set \(K\) has an infinite number of elements (see Banks et al. 1992), although this result does not hold for sets with finite elements. More to the point, the definition seems counterintuitive in that it emphasizes periodic orbits rather than aperiodicity, but the latter seems a much bett