Arithmetic of Unicritical Polynomial Maps

with derivative g b(w) = w n−1 , and use the conjugacy invariant b̂ = b . These normal forms (0.1) and (0.2) are related by the change of variable formula w = nz with b̂ = nĉ , and hence b = nc . (In particular, in the degree two case, b = b̂ is equal to 4c = 4ĉ .) If A is any ring contained in the complex numbers C , it will be convenient to use the non-standard notation A for the integral closure, the ring consisting of all complex numbers which satisfy a monic polynomial equation with coefficients in A . (See for example [AM].) Section 1 consists of statements about periodic orbits, which are proved in §2. The last section discusses the critically finite case.