Convergence of pinching deformations and matings of geometrically finite polynomials
Convergence of pinching deformations and matings of geometrically finite polynomials
复制标题
收缩变形的收敛性和几何有限多项式的配合
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通讯作者：
L. Tan
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作者：
Lei Tan Cergy;L. Tan
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.
