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<p>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.</p>

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The Escaping Set in Transcendental Dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月8日

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  • Walter Bergweiler,
  • Lasse Rempe

摘要

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.