Conformal measures and matings between Kleinian groups and quadratic polynomials

Volume 193 / 2007

Marianne Freiberger Fundamenta Mathematicae 193 (2007), 95-132 MSC: 37F35, 37F30, 37F10, 37F05, 37F45. DOI: 10.4064/fm193-2-1


Following results of McMullen concerning rational maps, we show that the limit set of matings between a certain class of representations of $C_2 \,\ast\, C_3$ and quadratic polynomials carries $\delta$-conformal measures, and that if the correspondence is geometrically finite then the real number $\delta$ is equal to the Hausdorff dimension of the limit set. Moreover, when $f$ is the limit of a pinching deformation $\{f_t\}_{0 \leq t < 1}$ we give sufficient conditions for the dynamical convergence of $\{f_t\}$.


  • Marianne FreibergerSchool of Mathematical Sciences
    Queen Mary, University of London
    Mile End Road
    London E1 4NS, UK
    MMP, Centre for Mathematical Sciences
    Wilberforce Road
    Cambridge CB3 0WA, UK

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