Geometry of the locus of polynomials of degree 4 with iterative roots

TL;DR

This paper investigates the geometric structure of the set of degree 4 complex polynomials that have polynomial iterative roots, providing a detailed description of their locus.

Contribution

It offers a novel geometric characterization of degree 4 polynomials with polynomial iterative roots, expanding understanding of polynomial iteration.

Findings

Describes the locus of degree 4 polynomials with iterative roots

Provides geometric insights into polynomial iteration

Characterizes conditions for existence of polynomial roots

Abstract

We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.