On a question of Eremenko concerning escaping components of entire functions

Abstract

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.

7 pages; 1 figure. V2: Final version (some minor changes)

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