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Unbounded domains of normality. (English) Zbl 0902.30021

Summary: Let \(f\) be a transcendental entire function of order less than \(1/2\). We introduce the method of “self-sustaining spread” to study the components of the set of normality of such a function. We give a new proof of the fact that any preperiodic or periodic component of the set of normality of \(f\) is bounded. We obtain the same conclusion for a wandering domain if the growth rate of \(f\) is never too small.

MSC:

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37F99 Dynamical systems over complex numbers
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