The exponential map is not recurrent (Q1077581)

Denote the exponential map by \(E(z)=e^ z\) and the n-th iterate of the map by \(E^ n\). The author proves that for almost all \(z\in {\mathbb{C}}\), the limit points of the orbit \(\{E^ n(z)\), \(n\geq 0\}\) are precisely the orbit of 0. This result has been obtained independently by \textit{M. Lyubich} [Usp. Mat. Nauk 41, 199-200 (1986)].