Dynamics of transcendental Henon maps. Part IV

Abstract:

In this course we cover the dynamics of transcendental Henon maps. A transcendental Henon map is an automorphisms of $\C^2$ of the form $F(z,w)=(f(z)+aw,z)$ with $f:\C\to\C$ entire transcendental  and $a\in\R$.

Escaping and Oscillating Wandering domains. We construct an example of a transcendental Henon map with a wandering domain whose orbits converge to infinity, and of a transcendental Henon map with n oscillating orbit of wandering domains.The first example is inspired by the construction of wandering domains in one variable while the second example is costructed using Runge approximation.