Newton maps as matings of cubic polynomials

TL;DR

This paper proves that many renormalizable cubic polynomials can be combined through mating to form Newton maps, supporting a broader conjecture about the structure of cubic Newton maps.

Contribution

It establishes the existence of matings between specific classes of cubic polynomials resulting in Newton maps, advancing understanding of their structural composition.

Findings

Matings exist between certain renormalizable cubic polynomials and other cubic polynomials with fixed critical points.

The resulting matings are shown to be Newton maps.

Supports the conjecture that all cubic Newton maps can be described as matings or captures.

Abstract

In this paper we prove existence of matings between a large class of renormalizable cubic polynomials with one fixed critical point and another cubic polynomial having two fixed critical points. The resulting mating is a Newton map. Our result is the first part towards a conjecture by Tan Lei, stating that all (cubic) Newton maps can be described as matings or captures.