A lot is known about the forward iterates of an analytic function which is bounded by 1 in modulus on the unit disk D. The Denjoy-Wolff Theorem describes their convergence properties and several authors, from the 1880's to the 1980's, have provided conjugations which yield very precise descriptions of the dynamics. Backward-iteration sequences are of a different nature because a point could have infinitely many preimages as well as none. However, if we insist in choosing preimages that are at a...

For an entire function $f$ let $N\left(z\right)=z-f\left(z\right)/f^{\prime }\left(z\right)$ be the Newton function associated to $f$. Each zero $\xi$ of $f$ is an attractive fixed point of $N$ and is contained in an invariant component of the Fatou set of the meromorphic function $N$ in which the iterates of $N$ converge to $\xi$. If $f$ has an asymptotic representation $f\left(z\right)\sim exp(-z^n),n\in \mathbb{N}$, in a sector $|argz|\<\epsilon$, then there exists an invariant component of the Fatou set where the iterates of $N$ tend to infinity. Such a component is called an invariant Baker domain.A question in the opposite direction...