# On the core entropy of Newton maps

## TL;DR

This paper introduces the concept of core entropy for postcritically-finite Newton maps, investigates its continuity properties, and reveals that unlike polynomial cases, the entropy function is not continuous across the family, with detailed analysis at generic parameters.

## Contribution

It defines core entropy for Newton maps and provides a complete characterization of its continuity behavior within this family.

## Key findings

- Entropy function is discontinuous in the Newton map family.
- Continuity of entropy is fully characterized at generic parameters.
- Contrasts with polynomial case where entropy is continuous.

## Abstract

In this paper, we define the core entropy for postcritically-finite Newton maps and study its continuity within this family. We show that the entropy function is not continuous in this family, which is different from the polynomial case studied by Thurston, Gao, Dudko- Schleicher, Tiozzo [Th+, GT, DS, Ti2], and describe completely the continuity of the entropy function at generic parameters.