We discuss how chaos conditions on maps carry over to their products. First we give a counterexample showing that the pro\-duct of two chaotic maps (in the sense of Devaney) need not be chaotic. We then remark that if two maps (or even one of them) exhibit sensitive dependence on initial conditions, so does their product; likewise, if two maps possess dense periodic points, so does their product. On the other side, the product of two topologically transitive maps need not be topologically transitive. We then give sufficient conditions under which the product of two chaotic maps is chaotic in the sense of Devaney .
Devaney's chaos, topological transitivity, sensitive dependence on initial conditions
DEĞİRMENCİ, NEDİM and KOÇAK, ŞAHİN
"Chaos in product maps,"
Turkish Journal of Mathematics: Vol. 34:
4, Article 14.
Available at: https://journals.tubitak.gov.tr/math/vol34/iss4/14