Abstract: We investigated the kneading sequence of Feigenbaum’s map, definited the notion about * productfor finite sequence of 0~1, and proved via the properties of * product that such infinite sequences must be uniformly almost periodic points of the shift map in the symbolic space. Furthermore, we deduced that the kneading sequence for every porder Feigenbaum’s map is a uniformly almost periodic point of the shift map but not a periodic one.

Key words: Feigenbaum’s map, renormalization operator, symbolic dynamical system, almost periodic properties