Conformal measures and matings between Kleinian groups and quadratic polynomials

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 -