Convergence of pinching deformations and matings of geometrically finite polynomials

Peter Haïssinsky, and Lei Tan. "Convergence of pinching deformations and matings of geometrically finite polynomials." Fundamenta Mathematicae 181.2 (2004): 143-188. <http://eudml.org/doc/283321>.

@article{PeterHaïssinsky2004,
abstract = {We give a thorough study of Cui's control of distortion technique in the analysis of convergence of simple pinching deformations, and extend his result from geometrically finite rational maps to some subset of geometrically infinite maps. We then combine this with mating techniques for pairs of polynomials to establish existence and continuity results for matings of polynomials with parabolic points. Consequently, if two hyperbolic quadratic polynomials tend to their respective root polynomials radially, and do not belong to conjugate limbs of the Mandelbrot set, then their mating exists and deforms continuously to the mating of the two root polynomials.},
author = {Peter Haïssinsky, Lei Tan},
journal = {Fundamenta Mathematicae},
keywords = {weakly hyperbolic maps; convergence of simple pinching deformations; geometrically infinite maps; mating techniques for pairs of polynomials},
language = {eng},
number = {2},
pages = {143-188},
title = {Convergence of pinching deformations and matings of geometrically finite polynomials},
url = {http://eudml.org/doc/283321},
volume = {181},
year = {2004},
}

TY - JOUR
AU - Peter Haïssinsky
AU - Lei Tan
TI - Convergence of pinching deformations and matings of geometrically finite polynomials
JO - Fundamenta Mathematicae
PY - 2004
VL - 181
IS - 2
SP - 143
EP - 188
AB - We give a thorough study of Cui's control of distortion technique in the analysis of convergence of simple pinching deformations, and extend his result from geometrically finite rational maps to some subset of geometrically infinite maps. We then combine this with mating techniques for pairs of polynomials to establish existence and continuity results for matings of polynomials with parabolic points. Consequently, if two hyperbolic quadratic polynomials tend to their respective root polynomials radially, and do not belong to conjugate limbs of the Mandelbrot set, then their mating exists and deforms continuously to the mating of the two root polynomials.
LA - eng
KW - weakly hyperbolic maps; convergence of simple pinching deformations; geometrically infinite maps; mating techniques for pairs of polynomials
UR - http://eudml.org/doc/283321
ER -