Orthogonality and the hausdorff dimension of the maximal measure

Abstract

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.