Dynamic rays of bounded-type entire functions

• 成果类型: Article
• 署名作者: Rottenfusser, Guenter; Rueckert, Johannes; Rempe, Lasse; Schleicher, Dierk
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.1.3
• 发表日期: 2011
• 页码: 77-125
• 关键词: transcendental entire-functions; Hausdorff Dimension; finite-order; julia sets; entire maps; hairs; Iteration; geometry; eremenko; points

摘要

We construct an entire function in the Eremenko-Lyubich class B whose Julia set has only bounded path-components. This answers a question of Eremenko from 1989 in the negative. On the other hand, we show that for many functions in B, in particular those of finite order, every escaping point can be connected to infinity by a curve of escaping points. This gives a partial positive answer to the aforementioned question of Eremenko, and answers a question of Fatou from 1926.