Coupled-expanding maps under small perturbations

This paper studies the C¹-perturbation problem of strictly A-coupled-expanding maps in finite-dimensional Euclidean spaces, where A is an irreducible transition matrix with one row-sum no less than 2. It is proved that under certain conditions strictly A-coupled-expanding maps are chaotic in the sense of Li-Yorke or Devaney under small C¹-perturbations. It is shown that strictly A-coupled-expanding maps are C¹ structurally stable in their chaotic invariant sets under certain stronger conditions. One illustrative example is provided with computer simulations.