Periodic points, multiplicities, and dynamical units.

Let φ (z) e C [z] be a polynomial of degree at least 2. The fixed points of the iterates of φ have been widely studied since the time of Julia and Fatou in order to analyze the dynamical System associated to φ. (See, for example, [2].) If φ (ζ) has coefficients in a number field K, these periodic points will generate interesting algebraic extensions of K. More precisely, if α e K is a periodic point for φ, then the map