In this paper the orthogonality properties of iterated polynomials are shown to remain valid in some cases for rational maps. Using a functional equation fulfilled by the generating function, the author shows that the Hausdorff dimension of the maximal measure is a real analytical function of the coefficients of an Axiom A rational map satisfying the property that all poles of ƒ and zeros of ƒ’(z) have multiplicity one.
Proceedings of the American Mathematical Society. Providence, RI. Vol. 98, no. 1 (sept. 1986), p. 51-55.