Newton maps of complex exponential functions and parabolic surgery

TL;DR

This paper introduces the concept of postcritically minimal Newton maps for complex exponential functions, establishing a dynamic correspondence with polynomial Newton maps, and develops a surgery tool for their analysis.

Contribution

It defines postcritically minimal Newton maps for complex exponentials and constructs a dynamics-preserving map linking them to polynomial Newton maps.

Findings

Introduction of postcritically minimal Newton maps

Construction of a dynamics-preserving mapping

Development of a surgery tool for analysis

Abstract

The paper deals with Newton maps of complex exponential functions and a surgery tool developed by P. Ha\"issinsky. The concept of "Postcritically minimal" Newton maps of complex exponential functions are introduced, analogous to postcritically finite Newton maps of polynomials. The dynamics preserving mapping is constructed between the space of postcritically finite Newton maps of polynomials and the space of postcritically minimal Newton maps of complex exponential functions.