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On a question of Eremenko concerning escaping components of entire functions

Lasse Rempe

Published 2006-10-15, updated 2007-03-16Version 2

Let f be an entire function with a bounded set of singular values, and suppose furthermore that the postsingular set of f is bounded. We show that every component of the escaping set I(f) is unbounded. This provides a partial answer to a question of Eremenko.

Comments: 7 pages; 1 figure. V2: Final version (some minor changes)
Journal: Bull. London Math. Soc. 39 (2007), no. 4, 661 - 666
Categories: math.DS, math.CV
Subjects: 37F10, 30D05
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