On The Notions of Mating

TL;DR

This paper explores various concepts of polynomial matings, analyzing their relationships, obstructions, and properties, including holomorphic motion, to deepen understanding of how polynomial pairs combine in complex dynamics.

Contribution

It introduces and relates different notions of polynomial matings, identifies obstructions, and proves properties like holomorphic motion for slow-mating, advancing theoretical understanding.

Findings

Identified and related various notions of polynomial matings.

Analyzed obstructions to polynomial matings.

Proved holomorphic motion properties of slow-mating.

Abstract

The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations between the polynomials and their matings are discussed and proved. Finally holomorphic motion properties of slow-mating are proved.