Reading escaping trees from Hubbard trees in Sn

TL;DR

This paper proves the connectedness of the parameter space for certain cubic polynomials and links escaping trees with Hubbard trees, advancing understanding in complex dynamics.

Contribution

It establishes the connectedness of the parameter space for monic centered cubic polynomials with a critical point of period 4 and relates escaping trees to Hubbard trees.

Findings

Parameter space of cubic polynomials with period 4 is connected.

Techniques apply to all periods n, generalizing the result.

Links between escaping trees and Hubbard trees are established.

Abstract

We prove that the parameter space of monic centered cubic polynomials with a critical point of exact period n=4 is connected. The techniques developed for this proof work for every n and provide an interesting relation between escaping trees of DeMarco-McMullen and Hubbard trees.