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arXiv · 1006.0222

On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Xavier Jarque
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Abstract

Let $E_{\la}(z)=\la {\rm exp}(z), \ λ\in \mathbb C$ be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $\la$, the set of points in $\mathbb C$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $E_{\la}$ with $\la$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

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Xavier Jarque. 2010-06-01. On the connectivity of the escaping set for complex exponential Misiurewicz parameters. https://arxiv.org/abs/1006.0222

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