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Nov 19, 2013 at 23:59 comment added Lasse Rempe The answer is positive if the function belongs to the class $\mathcal{B}$ where the set of singular values is bounded. (Here the real escaping set, if nonempty, must contain an interval of the form $[R,\infty)$ or $(-\infty,R]$.)
Nov 17, 2013 at 18:52 vote accept Sebastien Palcoux
Nov 17, 2013 at 18:46 comment added Sebastien Palcoux @AlexandreEremenko : yes
Nov 17, 2013 at 13:41 answer added Alexandre Eremenko timeline score: 5
Nov 17, 2013 at 13:10 comment added Alexandre Eremenko Stable on $R$ means $f(R)\subset R$?
Nov 17, 2013 at 9:04 history asked Sebastien Palcoux CC BY-SA 3.0