Steinmetz, Norbert2025-02-202025-02-202023-11-30http://hdl.handle.net/2003/4348010.17877/DE290R-25313In this paper, the classification of rational functions whose Julia sets are Jordan arcs or curves, which started in (Carleson and Gamelin in Complex dynamics, Springer, Berlin, 1993; Steinmetz in Math Ann 307:531–541, 1997), will be completed. The method of proof is based on two quasi-conformal surgery procedures, which enables shifting the critical points in simply connected (super-)attracting and parabolic basins into a single critical point of highest possible multiplicity.enComputational methods and function theory; 24(3)https://creativecommons.org/licenses/by/4.0/Julia setJordan curveParabolic fixed pointQuasi-conformal surgery510ArticleJulia-MengeJordanscher KurvensatzQuasikonforme AbbildungParabolische DifferentialgleichungFixpunkttheorie