Mating Siegel and Thurston quadratic polynomials

TL;DR

This paper proves that quadratic polynomials with bounded type Siegel disks can be mated with quadratic post-critically finite polynomials, expanding understanding of polynomial mating in complex dynamics.

Contribution

It establishes a new class of quadratic polynomials that are always mateable with post-critically finite polynomials, specifically those with bounded type Siegel disks.

Findings

Quadratic polynomials with bounded type Siegel disks are mateable with quadratic post-critically finite polynomials.

The result broadens the class of known mateable polynomials in complex dynamics.

Provides a new criterion for polynomial mating based on Siegel disk properties.

Abstract

We prove that a quadratic polynomial with a bounded type Siegel disk and a quadratic post-critically finite polynomial are always mateable.