发表机构
University of Liverpool; The University of Manchester; Center for Computing Sciences（利物浦大学; 曼彻斯特大学; 计算科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过构造逃逸集具有紧致连通分量（包括单点分量）的超越整函数，否证了Eremenko猜想，并面向一般读者介绍该问题及构造变体。
AI 中文摘要
超越整函数的逃逸集由那些在迭代下趋于无穷的点组成。Eremenko曾问这个集合的每个连通分量是否有界。在arXiv:2108.10256中，我们构造了逃逸集具有预定紧致连通分量的超越整函数；特别地，它可能有一个单点分量。这否证了该猜想。在本文中，我们面向一般数学读者介绍这个问题。我们还概述了构造的一个变体，其中预定的半带是一个振荡游荡域，且一个逃逸点位于其边界上。该叙述基于第二作者在2026年国际基础科学大会上的讲座。
英文摘要
The escaping set of a transcendental entire function consists of those points that tend to infinity under iteration. Eremenko asked whether every connected component of this set is unbounded. In arXiv:2108.10256, we constructed transcendental entire functions for which the escaping set has prescribed compact connected components; in particular, it may have a singleton component. This disproves the conjecture. In this note, we give an introduction to the problem, aimed at a general mathematical audience. We also sketch a variant of the construction in which a prescribed half-strip is an oscillating wandering domain and an escaping point lies on its boundary. The account is based on the second author's lecture at the 2026 International Congress of Basic Science.
Comments10 pages, 1 figure
