Geodesic
Dynamic rays of bounded-type entire functions
Günter Rottenfusser1 ; Johannes Rückert2 ; Lasse Rempe3 ; Dierk Schleicher4
1 Görresstraße 20<br/> 80798 München <br/>Germany
2 Jacobs University Bremen<br/> 28759 Bremen<br/>Germany
3 University of Liverpool<br/> Liverpool L69 7ZL<br/> United Kingdom
4 Jacobs University Bremen<br/>28759 Bremen<br/> Germany
Annals of mathematics, Tome 173 (2011) no. 1, pp. 77-125.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We construct an entire function in the Eremenko-Lyubich class $\mathcal{B}$ 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 $\mathcal{B}$, in particular those of finite order, every escaping point can be connected to $\infty$ 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.
DOI : 10.4007/annals.2011.173.1.3

Günter Rottenfusser 1 ; Johannes Rückert 2 ; Lasse Rempe 3 ; Dierk Schleicher 4

1 Görresstraße 20<br/> 80798 München <br/>Germany
2 Jacobs University Bremen<br/> 28759 Bremen<br/>Germany
3 University of Liverpool<br/> Liverpool L69 7ZL<br/> United Kingdom
4 Jacobs University Bremen<br/>28759 Bremen<br/> Germany 
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Günter Rottenfusser; Johannes Rückert; Lasse Rempe; Dierk Schleicher. Dynamic rays of bounded-type entire functions. Annals of mathematics, Tome 173 (2011) no. 1, pp. 77-125. doi : 10.4007/annals.2011.173.1.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.1.3/

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