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Branched coverings and cubic Newton maps

Lei Tan — 1997

Fundamenta Mathematicae

We construct branched coverings such as matings and captures to describe the dynamics of every critically finite cubic Newton map. This gives a combinatorial model of the set of cubic Newton maps as the gluing of a subset of cubic polynomials with a part of the filled Julia set of a specific polynomial (Figure 1).

Convergence of pinching deformations and matings of geometrically finite polynomials

Peter HaïssinskyLei Tan — 2004

Fundamenta Mathematicae

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...

On a theorem of Rees-Shishikura

Guizhen CuiWenjuan PengLei Tan — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

Rees-Shishikura’s theorem plays an important role in the study of matings of polynomials. It promotes Thurston’s combinatorial equivalence into a semi-conjugacy. In this work we restate and reprove Rees-Shishikura’s theorem in a more general form, which can then be applied to a wider class of postcritically finite branched coverings. We provide an application of the restated theorem.

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