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Conformal measures and matings between Kleinian groups and quadratic polynomials

Marianne Freiberger — 2007

Fundamenta Mathematicae

Following results of McMullen concerning rational maps, we show that the limit set of matings between a certain class of representations of C₂ ∗ C₃ and quadratic polynomials carries δ-conformal measures, and that if the correspondence is geometrically finite then the real number δ 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 $f_{t}$ .

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