Geodesic
Conformal measures and matings between Kleinian groups and quadratic polynomials
Marianne Freiberger1
1 School of Mathematical Sciences Queen Mary, University of London Mile End Road London E1 4NS, UK and MMP, Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WA, UK
Fundamenta Mathematicae, Tome 193 (2007) no. 2, pp. 95-132 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\{f_t\}$.
DOI : 10.4064/fm193-2-1
Keywords: following results mcmullen concerning rational maps limit set matings between certain class representations ast quadratic polynomials carries delta conformal measures correspondence geometrically finite real number delta equal hausdorff dimension limit set moreover limit pinching deformation leq sufficient conditions dynamical convergence

Marianne Freiberger 1

1 School of Mathematical Sciences Queen Mary, University of London Mile End Road London E1 4NS, UK and MMP, Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WA, UK 
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Marianne Freiberger. Conformal measures and matings between Kleinian groups and
quadratic polynomials. Fundamenta Mathematicae, Tome 193 (2007) no. 2, pp. 95-132. doi: 10.4064/fm193-2-1

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