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 $ainR$.

Classification of recurrent Fatou components. We show that for any invariant recurrent Fatou component $Omega$ there is a retraction $ ho:Omega ightarrowSigmasubset Omega$ where  $Sigma$ is an invariant limit manifold of rank 0, 1 or 2. If $Sigma $ has rank 0, $Omega$ is an attracting domain; If $Sigma$ has rank 2, $Omega$ is a rotation domain; if $Sigma$ has rank 1, then it is a rotational surface.