Rational rays and critical portraits of complex polynomials

TL;DR

This paper characterizes the rational lamination relations for complex polynomials with all cycles repelling and explores their location in parameter space, impacting the understanding of Julia set topology.

Contribution

It provides a detailed description of rational lamination equivalence relations and their parameter space realizations for polynomials with all cycles repelling.

Findings

Classification of rational lamination relations

Identification of parameter space regions with specified laminations

Implications for Julia set topology

Abstract

The aim of this work is to describe the equivalence relations in $\Q/\Z$ that arise as the rational lamination of polynomials with all cycles repelling. We also describe where in parameter space one can find a polynomial with all cycles repelling and a given rational lamination. At the same time we derive some consequences that this study has regarding the topology of Julia sets.