Conformal measures and matings between Kleinian groups and quadratic polynomials

• Autorzy: Marianne Freiberger
• Języki publikacji: EN

Abstrakty

EN

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 ${f_t}$.

Kategorie tematyczne

• 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
• 37F35: Conformal densities and Hausdorff dimension
• 37F10: Polynomials; rational maps; entire and meromorphic functions
• 37F05: Relations and correspondences
• 37F30: Quasiconformal methods and Teichm\"uller theory; Fuchsian and Kleinian groups as dynamical systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 193
• Numer: 2
• Strony: 95-132

Daty

wydano

2007

Twórcy

autor

Marianne Freiberger

• School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
• MMP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK

Identyfikatory

DOI

10.4064/fm193-2-1