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.


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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