Abstract

In this talk we use approximation theory to construct a transcendental entire function $f$ which has a sequence of bounded, simply connected, escaping wandering domains ${U_n}_{n geq 0}$. Furthermore, we show that for any pair of points $z,w$ in $U_1$ the hyperbolic distance in $U_{n+1}$ between $f^n(z)$ and $f^n(w)$ decreases but does not tend to 0 as n tends to infinity.