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

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.