Quasiconformal deformation of a ball

1992 ◽  
Vol 33 (1) ◽  
pp. 95-110
Author(s):  
V. I. Semenov
Keyword(s):  
Quasiconformal Deformation

scholarly journals Tessellation and Lyubich–Minsky laminations associated with quadratic maps, I: pinching semiconjugacies

2009 ◽  
Vol 29 (2) ◽  
pp. 579-612
Author(s):  
TOMOKI KAWAHIRA
Keyword(s):  
Julia Set ◽  
Julia Sets ◽  
Quadratic Maps ◽  
Quasiconformal Deformation ◽  
External Rays

AbstractWe construct tessellations of the filled Julia sets of hyperbolic and parabolic quadratic maps. The dynamics inside the Julia sets are then organized by tiles which play the role of the external rays outside. We also construct continuous families of pinching semiconjugacies associated with hyperbolic-to-parabolic degenerations without using quasiconformal deformation. Instead, we achieve this via tessellation and investigation of the hyperbolic-to-parabolic degeneration of linearizing coordinates inside the Julia set.

scholarly journals Subhyperbolic rational maps on boundaries of hyperbolic components

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yan Gao ◽  
Luxian Yang ◽  
Jinsong Zeng
Keyword(s):  
Critical Points ◽  
Rational Maps ◽  
Rational Map ◽  
Hyperbolic Component ◽  
Quasiconformal Deformation ◽  
Geometrically Finite

<p style='text-indent:20px;'>In this paper, we prove that every quasiconformal deformation of a subhyperbolic rational map on the boundary of a hyperbolic component <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{H} $\end{document}</tex-math></inline-formula> still lies on <inline-formula><tex-math id="M2">\begin{document}$ \partial \mathcal{H} $\end{document}</tex-math></inline-formula>. As an application, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components.</p>

scholarly journals Angles and quasiconformal mappings between manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4889-4896
Author(s):  
Jian-Feng Zhu
Keyword(s):  
Quasiconformal Mappings ◽  
Quasiconformal Deformation

In this paper we discuss the distortion of angles under quasiconformal deformation between manifolds. Moreover, we obtain some useful inequalities.

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