| dc.description |
Suppose ƒ : X* → X* is a morphism and u,v ∈ X*. For every nonnegative integer n, let z <sub> n </sub> be the longest common prefix of ƒ <sup>n</sup>(u) and ƒ <sup>n</sup>(v), and let u<sub>n</sub>,v<sub>n</sub> ∈ X* be words such that ƒ <sup>n</sup>(u) = z<sup>n</sup>u<sup>n</sup> and ƒ <sup>n</sup>(v) = z<sup>n</sup>v<sup>n</sup> . We prove that there is a positive integer q such that for any positive integer p, the prefixes of u <sub> n </sub> (resp. v <sub> n </sub>) of length p form an ultimately periodic sequence having period q. Further, there is a value of q which works for all words u,v ∈ X*. |
