Combinatorial properties of Newton maps

TL;DR

This paper develops a combinatorial model for all postcritically finite Newton maps of complex polynomials, enabling their classification based on combinatorial data.

Contribution

It introduces a comprehensive combinatorial framework for analyzing and classifying postcritically finite Newton maps of any degree.

Findings

Constructed a combinatorial model for postcritically finite Newton maps.

Enabled classification of these maps using combinatorial data.

Provided tools for understanding the dynamics of Newton's method in complex polynomials.

Abstract

This paper constructs a combinatorial model for all postcritically finite rational maps arising as the Newton's method of a complex polynomial. This model is used in [LMS] to give a combinatorial classification of postcritically finite Newton maps of any degree.