Inverse polynomial images which consists of two Jordan arcs - An algebraic solution

TL;DR

This paper provides an explicit algebraic characterization of inverse polynomial images of the interval [-1,1] that consist of two Jordan arcs, focusing on the endpoints of these arcs.

Contribution

It introduces a new explicit polynomial equation describing the endpoints of inverse polynomial images comprising two Jordan arcs.

Findings

Derived an explicit polynomial equation for the endpoints.

Characterized inverse polynomial images with two Jordan arcs.

Enhanced understanding of polynomial inverse images in complex analysis.

Abstract

Inverse polynomial images of $[-1,1]$, which consists of two Jordan arcs, are characterised by an explicit polynomial equation for the four endpoints of the arcs.