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Conformal Geometry and Dynamics

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Cantor bouquets in spiders' webs


Author: Yannis Dourekas
Journal: Conform. Geom. Dyn. 24 (2020), 1-28
MSC (2010): Primary 37F10
DOI: https://doi.org/10.1090/ecgd/346
Published electronically: January 7, 2020
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Abstract: For many transcendental entire functions, the escaping set has the structure of a Cantor bouquet, consisting of uncountably many disjoint curves. Rippon and Stallard showed that there are many functions for which the escaping set has a new connected structure known as an infinite spider's web. We investigate a connection between these two topological structures for a certain class of sums of exponentials.


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Additional Information

Yannis Dourekas
Affiliation: School of Mathematics and Statistics, Open University, Milton Keynes MK7 6AA, United Kingdom
Email: ioandour@gmail.com

DOI: https://doi.org/10.1090/ecgd/346
Received by editor(s): September 20, 2019
Published electronically: January 7, 2020
Article copyright: © Copyright 2020 American Mathematical Society