On product property of Devaney chaos maps in topology space

This paper discusses whether the product of chaotic maps(in the sense of Devaney) is chaotic.First it remarks that if maps posse dense periodic points,so does their product.But the product of topologically transitive maps need not be topologically transitive.Then we give a counterexample showing that the product of chaotic maps need not be chaotic.Finally we introduce the concept of topologically mixing and give sufficient conditions under which the product of two chaotic maps is chaotic.