A note on the topology of escaping endpoints

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 trans...

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Bibliographic Details
Published inarXiv.org
Main Author Lipham, David Sumner
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.04.2020
Subjects
Entire functions
Mathematics - Dynamical Systems
Mathematics - General Topology
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1908.10985