Rescaling Limits in Non-Archimedean Dynamics

TL;DR

This paper proves a finiteness theorem for rescaling limits in non-Archimedean dynamics, enhancing understanding of how rational maps behave under parameter changes over non-Archimedean fields.

Contribution

It introduces a finiteness result for the set of rescalings in analytic families of rational maps over non-Archimedean fields, complementing prior work by Kiwi.

Findings

Finiteness of rescaling limits established

Results apply to analytic one-parameter families

Advances understanding of non-Archimedean rational dynamics

Abstract

Suppose $\{f_t\}$ is an analytic one-parameter family of rational maps defined over a non-Archimedean field $K$. We prove a finiteness theorem for the set of rescalings for $\{f_t\}$. This complements results of J. Kiwi.