Chebyshev Polynomials on Generalized Julia Sets

Let (f(n))(n=1)(infinity) be a sequence of non-linear polynomials satisfying some mild conditions. Furthermore, let F-m(z) : = (f(m) circle f(m-1) ... circle f(1)) (z) and rho(m) be the leading coefficient of F-m. It is shown that on the Julia set J((fn)), the Chebyshev polynomial of degree F-m is of the form F-m(z)/rho(m) - tau(m) for all m is an element of N where tau(m) is an element of C. This generalizes the result obtained for autonomous Julia sets in Kamo and Borodin (Mosc. Univ. Math. Bull. 49:44-45, 1994).