Dynamic rays of bounded-type entire functions | Annals of Mathematics

Abstract We construct an entire function in the Eremenko-Lyubich class  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 , in particular those of finite order, every escaping point can be connected to ∞ 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.

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数学年刊(Annals of Mathematics)

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