Abstract: Following Feigenbaum’s kneading subshifts, we introduced the notion of * product subshift under the wider sense. By investigating the relationship between * product subshift and substitution subshift, and by using the known results on substitution subshifts, we proved that every * product subshift is minimal, uniquely ergodic, nonchaotic in the sense of Li and Yorke and has zero topological entropy, from which we deduced that every Feigenbaum’s kneading subshift also exhibits the above properties.

Key words: Feigenbaum mapping, * product subshift, uniquely ergodic, LiYorke chaos, topological entropy