1LATP//CMI Université de Provence 39, rue Frédéric Joliot-Curie 13453 Marseille Cedex 13, France 2Unité CNRS-UMR 8088 Département de Mathématiques Université de Cergy-Pontoise 2, avenue Adolphe Chauvin 95302 Cergy-Pontoise Cedex, France
Fundamenta Mathematicae, Tome 181 (2004) no. 2, pp. 143-188
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.
Keywords:
thorough study cuis control distortion technique analysis convergence simple pinching deformations extend his result geometrically finite rational maps subset geometrically infinite maps combine mating techniques pairs polynomials establish existence continuity results matings polynomials parabolic points consequently hyperbolic quadratic polynomials tend their respective root polynomials radially belong conjugate limbs mandelbrot set their mating exists deforms continuously mating root polynomials
Affiliations des auteurs :
Peter Haïssinsky
1
;
Lei Tan
2
1
LATP//CMI Université de Provence 39, rue Frédéric Joliot-Curie 13453 Marseille Cedex 13, France
2
Unité CNRS-UMR 8088 Département de Mathématiques Université de Cergy-Pontoise 2, avenue Adolphe Chauvin 95302 Cergy-Pontoise Cedex, France
@article{10_4064_fm181_2_4,
author = {Peter Ha{\"\i}ssinsky and Lei Tan},
title = {Convergence of pinching deformations and
matings of geometrically finite polynomials},
journal = {Fundamenta Mathematicae},
pages = {143--188},
year = {2004},
volume = {181},
number = {2},
doi = {10.4064/fm181-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm181-2-4/}
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AU - Peter Haïssinsky
AU - Lei Tan
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JO - Fundamenta Mathematicae
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%A Peter Haïssinsky
%A Lei Tan
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matings of geometrically finite polynomials
%J Fundamenta Mathematicae
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Peter Haïssinsky; Lei Tan. Convergence of pinching deformations and
matings of geometrically finite polynomials. Fundamenta Mathematicae, Tome 181 (2004) no. 2, pp. 143-188. doi: 10.4064/fm181-2-4
