Julia sets, Jordan curves and quasi-circles
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Date
2023-11-30
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Abstract
In 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.
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Julia set, Jordan curve, Parabolic fixed point, Quasi-conformal surgery
Subjects based on RSWK
Julia-Menge, Jordanscher Kurvensatz, Quasikonforme Abbildung, Parabolische Differentialgleichung, Fixpunkttheorie