Hausdorff dimension and conformal dynamics. II: Geometrically finite rational maps (Q1596286)

Let \(f:\widehat\mathbb{C}\to \widehat\mathbb{C}\) be a rational map on the Riemann sphere, of degree \(d\geq 2\). The authors study the equality of several dynamically defined dimensions for \(f\), and their variation as a function of \(f\). The authors also develop a new technique that reduces the study of parabolic bifurcations of rational maps to the case of Möbius transformations. For Part I, cf. J. Differ. Geom. 51, 471-515 (1999; Zbl 1023.37028), for Part III, see Am. J. Math. 120, 691-721 (1998; Zbl 0953.30026).