# A characterization of postcritically minimal Newton maps of complex exponential functions

## TL;DR

This paper establishes a unique correspondence between certain polynomial Newton maps and entire Newton maps of exponential type, preserving their dynamics and Julia set structures, using a novel surgery method.

## Contribution

It introduces a canonical bijection linking postcritically finite polynomial Newton maps to postcritically minimal exponential Newton maps, advancing the understanding of their dynamics.

## Key findings

- Established a bijection preserving Julia set dynamics
- Developed a surgery tool for mapping between classes
- Unified polynomial and exponential Newton map classifications

## Abstract

We obtain a unique, canonical one-to-one correspondence between the space of marked postcritically finite Newton maps of polynomials and the space of postcritically minimal Newton maps of entire maps that take the form $p(z) \text{exp}(q(z))$ for $p(z)$, $q(z)$ polynomials and $\text{exp}(z)$, the complex exponential function. This bijection preserves the dynamics and embedding of Julia sets and is induced by a surgery tool developed by Ha\"issinsky.