# Iteration at the Boundary of Newton Maps

## TL;DR

This paper investigates the boundary behavior of holomorphic families of Newton maps of degree at least 3, analyzing their measure limits and rescaling limits through Berkovich dynamics.

## Contribution

It provides new estimates for the weak limits of maximal measures and a comprehensive description of rescaling limits for these families.

## Key findings

- Estimate of weak limits of maximal measures
- Complete description of rescaling limits
- Application of Berkovich dynamics to Newton maps

## Abstract

Let $\{N_t\}$ be a holomorphic family of degree $d\ge 3$ Newton maps. By studying the related Berkovich dynamics, we obtain an estimate of the weak limit of the maximal measures of $N_t$. Moreover, we give a complete description of the rescaling limits for $\{N_t\}$.