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 we give sufficient conditions for the dynamical convergence of .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-2-1,
author = {Marianne Freiberger},
title = {Conformal measures and matings between Kleinian groups and quadratic polynomials},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {95-132},
zbl = {1131.37053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-2-1}
}
Marianne Freiberger. Conformal measures and matings between Kleinian groups and quadratic polynomials. Fundamenta Mathematicae, Tome 193 (2007) pp. 95-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-2-1/