Dynamic rays of bounded-type entire functions

Günter Rottenfußer; Johannes Rueckert; Lasse Rempe; Dierk Schleicher

doi:10.4007/annals.2011.173.1.3

Dynamic rays of bounded-type entire functions

Günter Rottenfußer
, Johannes Rueckert
, Lasse Rempe
, Dierk Schleicher

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 ∞ 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.

Original language	English
Pages (from-to)	77-125
Number of pages	49
Journal	Annals of Mathematics
Volume	173
Issue number	1
DOIs	https://doi.org/10.4007/annals.2011.173.1.3
Publication status	Published - 4 Jan 2011

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10.4007/annals.2011.173.1.3

Cite this

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AU - Schleicher, Dierk

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AB - 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 ∞ 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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EP - 125

JO - Annals of Mathematics

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Dynamic rays of bounded-type entire functions

Abstract

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