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Repulsive periodic points of meromorphic functions. (English) Zbl 0865.30040
One well-known and fundamental result in iteration theory of rational, entire and meromorphic functions states that the repulsive periodic points are dense in the Julia set. Whereas the proof in the rational case is elementary, the original proofs in the other cases (first given by I. N. Baker) both use Ahlfors’ theory on covering surfaces. Recently W. Schwick gave a proof in the entire case using only standard Nevanlinna theory. In the present paper it is shown that his proof extends easily to meromorphic functions with at most countably many essential singularities in spite of the fact that the Julia set of meromorphic functions arise in a rather different way. Another result deals with composite meromorphic functions.
Reviewer: A.Bolsch (Berlin)

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37F99 Dynamical systems over complex numbers
30D30 Meromorphic functions of one complex variable, general theory
39B32 Functional equations for complex functions
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