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arXiv · 1511.08440

On postsingularly finite exponential maps

Walter Bergweiler
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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 $0<|\lambda|\leq r$ 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 $\infty$.

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Walter Bergweiler. 2015-11-26. On postsingularly finite exponential maps. https://doi.org/10.1007/s40598-016-0056-4

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