A transcendental Henon map is an automorphism of $\mathbb{C}^2$ with constant Jacobian $\delta$ which has the special form

$F(z,w)=(f(z)-\delta w, z)$

where $f:\mathbb{C}\rightarrow\mathbb{C}$ is an entire transcendental map.

We will present the basic dynamical features of such a map, including a classification of the recurrent Fatou components, and show examples of transcendental Henon maps with Baker domains, with wandering domains whose orbits converge to infinity, and with wandering domains with oscillating orbits.

This is joint work with L. Arosio, J-E Fornaess and H. Peters.