Orthogonality and the Hausdorff dimension of the maximal measure

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 f f and zeros of f ′ ( z ) f’(z) have multiplicity one.