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arXiv · 0810.2260

Rational functions with real multipliers

Alexandre Eremenko·Sebastian van Strien
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Abstract

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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Alexandre Eremenko, Sebastian van Strien. 2008-10-13. Rational functions with real multipliers. https://arxiv.org/abs/0810.2260

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