This survey summarizes findings on the escaping set in transcendental dynamics and its significance.
The escaping set of an entire function consists of the points in the complex plane that tend to infinity under iteration. This set plays a central role in the dynamics of transcendental entire functions. The goal of this survey is to explain this role, to summarise some of the main results in the area, and to identify a number of open questions.
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Bergweiler et al. (2025) studied this question.
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