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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 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 .
Marianne Freiberger. "Conformal measures and matings between Kleinian groups and quadratic polynomials." Fundamenta Mathematicae 193.2 (2007): 95-132. <http://eudml.org/doc/282887>.
@article{MarianneFreiberger2007, abstract = {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 $\{f_t\}$.}, author = {Marianne Freiberger}, journal = {Fundamenta Mathematicae}, keywords = {conformal measure; mating; Kleinian group}, language = {eng}, number = {2}, pages = {95-132}, title = {Conformal measures and matings between Kleinian groups and quadratic polynomials}, url = {http://eudml.org/doc/282887}, volume = {193}, year = {2007}, }
TY - JOUR AU - Marianne Freiberger TI - Conformal measures and matings between Kleinian groups and quadratic polynomials JO - Fundamenta Mathematicae PY - 2007 VL - 193 IS - 2 SP - 95 EP - 132 AB - 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 ${f_t}$. LA - eng KW - conformal measure; mating; Kleinian group UR - http://eudml.org/doc/282887 ER -