Enumerating the basins of infinity of cubic polynomials

TL;DR

This paper investigates the complex dynamics of cubic polynomials focusing on their basins of infinity, and systematically classifies conjugacy classes based on combinatorial data.

Contribution

It introduces a method to enumerate topological conjugacy classes of cubic polynomials with specified combinatorial structures.

Findings

Classification of conjugacy classes achieved

Enumeration method for cubic polynomial dynamics developed

Insights into the structure of basins of infinity provided

Abstract

We study the dynamics of cubic polynomials restricted to their basins of infinity, and we enumerate topological conjugacy classes with given combinatorics.