An entire function with simply and multiply connected wandering domains

TL;DR

This paper constructs an entire function demonstrating the coexistence of simply and multiply connected wandering domains within the set of fast escaping points, expanding understanding of complex dynamics in entire functions.

Contribution

It introduces a novel construction of an entire function with both simply and multiply connected wandering domains, extending previous work by Kisaka and Shishikura.

Findings

Existence of an entire function with both types of wandering domains.

Both domains are contained in the set of fast escaping points.

The construction modifies prior methods to achieve this coexistence.

Abstract

We modify a construction of Kisaka and Shishikura to show that there exists an entire function which has both a simply connected and a multiply connected wandering domain. Moreover, these domains are contained in the set of fast escaping points.