Weak N\'{e}ron models for cubic polynomial maps over a non-Archimedean field

TL;DR

This paper provides an effective criterion to determine whether cubic polynomial maps over non-Archimedean fields admit weak Néron models, aiding in the classification of such dynamical systems.

Contribution

It introduces a new practical criterion for verifying the existence of weak Néron models for cubic polynomials over non-Archimedean fields.

Findings

Criterion effectively distinguishes polynomials with weak Néron models

Simplifies the verification process for non-Archimedean dynamics

Contributes to the classification of polynomial dynamical systems

Abstract

The aim of this note is to give an effective criterion to verify whether a cubic polynomial over a non-Archimedean field has a weak N\'{e}ron model or not.