# Oscillating Wandering Domains for Functions with Escaping Singular Values

## TL;DR

This paper constructs a transcendental entire function with a bounded singular set that exhibits a wandering domain, where all singular values escape to infinity, advancing understanding of complex dynamics.

## Contribution

It introduces a new example of a transcendental entire function with a bounded singular set and a wandering domain, where all singular values escape to infinity.

## Key findings

- Existence of a transcendental entire function with a wandering domain.
- All singular values of the constructed function escape to infinity.
- The function has a bounded singular set.

## Abstract

We construct a transcendental entire $f:\mathbb{C}\rightarrow\mathbb{C}$ such that (1) $f$ has bounded singular set, (2) $f$ has a wandering domain, and (3) each singular value of $f$ escapes to infinity under iteration by $f$.