On Two-Sided Infinite Fixed Points of Morphisms

Let be a nite alphabet, and let h : ! be a morphism. Finite and innnite xed points of morphisms | i.e., those words w such that h(w) = w | play an important role in formal language theory. Head characterized the nite xed points of h, and later, Head and Lando characterized the one-sided innnite xed points of h. Our paper has two main results. First, we complete the characterization of xed points of morphisms by describing all two-sided innnite xed points of h, for both the \pointed" and \unpointed" cases. Second, we completely characterize the solutions to the equation h(xy) = yx in nite words.