Devaney Chaos and Li-Yorke sensitivity for product systems (Q2859353)

The notions of Li-Yorke sensitivity and chaos in the sense of Devaney are considered for Cartesian product systems. For a finite product of topological dynamical systems, it is shown that the product is mixing and Devaney chaotic if and only if each factor system is. For countably infinite products an additional condition enters the picture, and it is shown that such a product is mixing and Devaney chaotic if and only if each factor map is mixing and Devaney chaotic and the supremum of the set of minimal periods across all the systems is finite. Li-Yorke sensitivity is shown to follow from having any factor system that is Li-Yorke sensitive.