Teichmüller spaces and normal forms associated to wandering domains

We study the dynamical Teichmüller space $\mathcal{T}(U,f)$ associated to a wandering domain $U$ of an entire function $f$. We show that a discrete grand orbit relation in $U$ forces $\mathcal{T}(U,f)$ to be infinite dimensional, thereby answering a question of Fagella–Henriksen. We further describe the geometry of these spaces by developing normal forms for the dynamics on wandering domains, yielding global linearising coordinates in the discrete case and power-type dynamics between annuli in the indiscrete case.