Arithmetic of Unicritical Polynomial Maps

TL;DR

This paper investigates the dynamics of complex unicritical polynomial maps of degree at least two, focusing on their arithmetic properties and how the presence of a single critical point influences their behavior.

Contribution

It provides new insights into the arithmetic structure and dynamical properties of unicritical polynomial maps, a class with a single critical point.

Findings

Characterization of the critical orbit structure

Relations between critical points and map dynamics

Implications for the parameter space of unicritical polynomials

Abstract

This note will study complex polynomial maps of degree $n\ge 2$ with only one critical point.