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Conformal measures and matings between Kleinian groups and quadratic polynomials

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Freiberger M.

Fundamenta Mathematicae

2007

tom 193

nr 2

95-132

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 ${f_t}_{0≤t<1}$ we give sufficient conditions for the dynamical convergence of ${f_t}$.

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1 Fundamenta Mathematicae

1 Freiberger M.

1 2007

Wyniki wyszukiwania

Conformal measures and matings between Kleinian groups and quadratic polynomials