Dynamics of transcendental Henon maps. Part II

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 $a\in\R$.

Classification of recurrent Fatou components. We show that for any invariant recurrent Fatou component $\Omega$ there is a retraction $\rho:\Omega \rightarrow\Sigma\subset \Omega$ 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.