TL;DR
This paper explores the topological structures of escaping sets in transcendental entire functions, focusing on the relationship between Cantor bouquets and spider's webs in sums of exponentials.
Contribution
It establishes a connection between Cantor bouquets and spider's webs for a specific class of exponential sums, advancing understanding of their topological structures.
Findings
Escaping sets can form Cantor bouquets or spider's webs.
A link between these two structures is demonstrated for certain exponential sums.
The results deepen the understanding of the topology of escaping sets in complex dynamics.
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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