Stallard, Gwyneth M. Meromorphic functions whose Julia sets contain a free Jordan arc. (English) Zbl 0793.30024 Ann. Acad. Sci. Fenn., Ser. A I, Math. 18, No. 2, 273-298 (1993). 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 Cited in 8 Documents 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 Keywords:Julia set; meromorphic function PDFBibTeX XMLCite \textit{G. M. Stallard}, Ann. Acad. Sci. Fenn., Ser. A I, Math. 18, No. 2, 273--298 (1993; Zbl 0793.30024) Full Text: EuDML EMIS