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Infinite limits in the iteration of entire functions. (English) Zbl 0642.30021
If f is a transcendental entire function and D is a non-wandering component of the set of normality of the iterates of f such that f $$n\to \infty$$ in D then log$$| f$$ $$n(z)| =O(n)$$ as $$n\to \infty$$ for z in D. For a wandering component the convergence of f n to $$\infty$$ in D may be arbitrarily fast.
Reviewer: I.N.Baker

##### MSC:
 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable 37B99 Topological dynamics
##### Keywords:
entire function; iterates; wandering domain; rate of convergence
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##### References:
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