HAUSDORFF AND CONFORMAL MEASURES ON JULIA SETS WITH A RATIONALLY INDIFFERENT PERIODIC POINT

We show that the Hausdorff dimension delta of a non-hyperbolic Julia set J(T) without critical points can be expressed by the smallest zero of the pressure function t bar-arrow-pointing-right P(T, - t log\T'\). This result is similar to the Bowen-Manning-McCluskey formula. The Hausdorff dimension is also shown to be the smallest exponent t is-an-element-of R for which a t-conformal measure in the sense of Sullivan exists. We also prove uniqueness properties of t-conformal measures, and we prove the absolute continuity of the Hausdorff measure H-delta with respect to any delta-conformal measure.