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Meromorphic functions whose Julia sets contain a free Jordan arc. (English) Zbl 0793.30024

In the main result of this paper we show that if the Julia set of a meromorphic function \(f\) contains a free analytic Jordan arc then it must be in fact a straight line, circle, segment of a straight line or an arc of a circle. If \(f\) is transcendental then the Julia set is unbounded and so consists of one or two straight line segments. We construct examples of functions whose Julia sets are of this form.
Reviewer: Gwyneth M.Stallard

MSC:

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
26A18 Iteration of real functions in one variable
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