Wandering Domains in $\mathbb{C}\times \mathbb{R}$

TL;DR

This paper constructs and modifies maps on  with wandering domains and Fatou components using approximation theory, revealing complex dynamical behaviors in .

Contribution

It introduces new constructions of maps on  with wandering domains and Fatou components, expanding understanding of complex dynamics in higher dimensions.

Findings

Constructed maps with wandering domains in .

Modified constructions to produce maps with multiple attracting Fatou components.

Demonstrated existence of maps with infinitely many wandering domains.

Abstract

Approximation theory of entire functions has been used to demonstrate the construction of a map on $\mathbb{C}\times\mathbb{R}$ having wandering domains. We also present suitable modification to this construction that helps in obtaining maps with similar characteristics such as infinitely many attracting Fatou components, infinitely many wandering domains having common paths, etc.