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arXiv · 1908.10985

A note on the topology of escaping endpoints

David Sumner Lipham
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Abstract

We study topological properties of the escaping endpoints and fast escaping endpoints of the Julia set of complex exponential $\exp(z)+a$ when $a\in (-\infty,-1)$. We show neither space is homeomorphic to the whole set of endpoints. This follows from a general result stating that for every transcendental entire function $f$, the escaping Julia set $I(f)\cap J(f)$ is first category.

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David Sumner Lipham. 2019-08-28. A note on the topology of escaping endpoints. https://doi.org/10.1017/etds.2019.111

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