Unicritical polynomial maps with rational multipliers

TL;DR

This paper proves that unicritical polynomial maps with only rational multipliers are either power maps or Chebyshev maps, supporting Milnor's conjecture about rational maps with integer multipliers.

Contribution

It establishes a classification of unicritical polynomial maps with rational multipliers, confirming a special case of Milnor's conjecture.

Findings

Unicritical polynomial maps with rational multipliers are either power maps or Chebyshev maps.

Supports Milnor's conjecture regarding rational maps with integer multipliers.

Provides a classification result in complex dynamics.

Abstract

In this article, we prove that every unicritical polynomial map that has only rational multipliers is either a power map or a Chebyshev map. This provides some evidence in support of a conjecture by Milnor concerning rational maps whose multipliers are all integers.