Dynamic rays of bounded-type entire functions

Details Dynamic rays of bounded-type entire functions Dynamic rays of bounded-type entire functions

2007-04-24

arxiv.org/abs/0704.3213v2

Ann. of Math. 173 (2011), no. 1, 77-125

Mathematics

Dynamical Systems

42 pages, 9 figures. V2. General revisions and corrections. Definition of the class \B_{\log} harmonized with other papers; so

Scientific paper

10.4007/annals.2010.173.1.3

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 $\infty$ 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.

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