$J$-Stability of immediately expanding rational maps in non-Archimedean dynamical systems

TL;DR

This paper proves the $J$-stability of immediately expanding rational maps in non-Archimedean dynamical systems, extending classical complex dynamics results to a non-Archimedean setting.

Contribution

It establishes the analogue of $J$-stability for immediately expanding rational maps over non-Archimedean fields, a significant extension of complex dynamical systems theory.

Findings

Proves $J$-stability for immediately expanding rational maps in non-Archimedean fields

Extends classical $J$-stability results to non-Archimedean dynamics

Provides foundational results for non-Archimedean dynamical systems

Abstract

The aim of this paper is to show $J$-stability of immediately expanding rational maps over an algebraically closed, complete, and non-Archimedean field, which is an analogue of R. Man\~e, P. Sad, and D. Sullivan's theorem of $J$-stability in complex dynamical systems.