Hausdorff measures on Julia sets of subexpanding rational maps (Q1196334)

A subexpanding analytic endomorphism of the Riemann sphere is a rational map \(R\) which is expanding on the intersection of the Julia set \(J(R)\) with the \(\omega\)-limit set of critical points. It is shown in the paper that for such maps there is exactly one conformal measure \(m\) in the sense of \textit{D. Sullivan} [Geometric dynamics, Proc. int. Symp., Rio de Janeiro/Brazil 1981, Lect. Notes Math. 1007, 725-752 (1983; Zbl 0524.58024)] on \(J(R)\). Its dimension of conformality agrees with the Hausdorff and Box dimensions. Moreover, the conformal measure is a multiple of the Hausdorff measure, and there exists a unique ergodic, \(R\)-invariant measure equivalent to \(m\).