Dynamics of transcendental Henon maps. Part I

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 $a\in\R$.

Different definitions of normality for holomorphic functions in $\C^2$. Basic features of holomorphic  dynamics in $\C^2$. Existence of saddle points for transcendental Henon maps. Proof of the non-emptyness of the Julia set.