COUPLED-EXPANDING MAPS AND MATRIX SHIFTS

For an irreducible transition matrix A of size m x m, which is not a permutation, a map f : X -> X is said to be strictly A-coupled-expanding if there are nonempty sets V-1,..., V-m subset of X such that the distance between any two of them is positive and f(Vi) superset of V-j holds whenever a(ij) = 1. This paper presents two theorems that give sufficient conditions for a strictly A-coupled-expanding map to be chaotic on part of its domain in the sense of, respectively, Auslander and Yorke and Devaney. These results improve on the work of Zhang and Shi [2010]. An example is provided to illustrate that the class of maps the new theorems apply to is significantly wider.