On postsingularly finite exponential maps

Abstract

We consider parameters $\lambda$ for which $0$ is preperiodic under the map $z\mapsto \lambda e^z$. Given $k$ and $l$, let $n(r)$ be the number of $\lambda$ satisfying $0<|\lambda |\le r$ such that $0$ is mapped after $k$ iterations to a periodic point of period $l$. We determine the asymptotic behavior of $n(r)$ as $r$ tends to $\infty$.

16 pages

References in corpus (1)

• Triviality of fibers for Misiurewicz parameters in the exponential family