Oscillating Wandering Domains for p-Adic Transcendental Entire Maps

TL;DR

This paper presents examples of transcendental entire maps over p-adic complex numbers that exhibit oscillating wandering Fatou components, expanding understanding of dynamical behaviors in non-Archimedean settings.

Contribution

It introduces the first known examples of oscillating wandering domains for p-adic transcendental entire maps, a phenomenon previously unobserved in this context.

Findings

Existence of oscillating wandering Fatou components in p-adic dynamics

Construction of specific transcendental entire maps with these properties

New insights into non-Archimedean dynamical systems

Abstract

We give examples of transcendental entire maps over $\mathbb{C}_p$ having an oscillating wandering Fatou component.