Laminations from the Main Cubioid

TL;DR

This paper characterizes the laminations associated with polynomials in the Main Cubioid, a set defined by specific properties related to the cubic connectedness locus, expanding understanding of their combinatorial structure.

Contribution

It describes the set of laminations corresponding to polynomials in the Main Cubioid, linking geometric properties to combinatorial models.

Findings

Identification of laminations associated with the Main Cubioid

Characterization of the combinatorial structure of these laminations

Insights into the properties of cubic polynomials in the closure of the Principal Hyperbolic Domain

Abstract

According to a recent paper \cite{bopt13}, polynomials from the closure $\bar{\rm PHD}_3$ of the {\em Principal Hyperbolic Domain} ${\rm PHD}_3$ of the cubic connectedness locus have a few specific properties. The family $\mathrm{CU}$ of all polynomials with these properties is called the \emph{Main Cubioid}. In this paper we describe the set $\mathrm{CU}^c$ of laminations which can be associated to polynomials from $\mathrm{CU}$.