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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
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