Rational functions with real multipliers

Details Rational functions with real multipliers Rational functions with real multipliers

2008-10-13

arxiv.org/abs/0810.2260v1

Trans. AMS, 363, 12 (2011) 6453-6463

Mathematics

Dynamical Systems

16 pages 1 figure

Scientific paper

Let f be a rational function such that the multipliers of all repelling
periodic points are real. We prove that the Julia set of such a function
belongs to a circle. Combining this with a result of Fatou we conclude that
whenever J(f) belongs to a smooth curve, it also belongs to a circle. Then we
discuss rational functions whose Julia sets belong to a circle.

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